UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                  SCHEDULE 13G

                    UNDER THE SECURITIES EXCHANGE ACT OF 1934
                               (AMENDMENT NO. 1)*

                         UNITED THERAPEUTICS CORPORATION
--------------------------------------------------------------------------------
                                (Name of Issuer)

                     Common Stock, $0.01 Par Value Per Share
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    91307C102
                                 (CUSIP Number)

                                December 31, 2004
                      (Date of Event which Requires Filing
                               of this Statement)



Check the appropriate box to designate the rule pursuant to which this Schedule
is filed:

                  [ ]  Rule 13d-1(b)
                  [X]  Rule 13d-1(c)
                  [ ]  Rule 13d-1(d)


*The remainder of this cover page shall be filled out for a reporting person's
initial filing on this form with respect to the subject class of securities, and
for any subsequent amendment containing information which would alter the
disclosures provided in a prior cover page.

The information required on the remainder of this cover page shall not be deemed
to be "filed" for the purpose of Section 18 of the Securities Exchange Act of
1934 ("Act") or otherwise subject to the liabilities of that section of the Act
but shall be subject to all other provisions of the Act (however, see the
Notes).


                                  Page 1 of 12




CUSIP No. 91307C102                   13G                    Page 2 of 12 Pages


________________________________________________________________________________
1.   NAME OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

     S.A.C. Capital Advisors, LLC

________________________________________________________________________________
2.   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                 (a)  [_]
                                                                 (b)  [X]

________________________________________________________________________________
3.   SEC USE ONLY



________________________________________________________________________________
4.   CITIZENSHIP OR PLACE OF ORGANIZATION

     Delaware

________________________________________________________________________________
  NUMBER OF    5.   SOLE VOTING POWER
                    
   SHARES           0
               _________________________________________________________________
BENEFICIALLY   6.   SHARED VOTING POWER
                    
  OWNED BY          400,000 (see Item 4)
               _________________________________________________________________
    EACH       7.   SOLE DISPOSITIVE POWER
                    
  REPORTING         0
               _________________________________________________________________
   PERSON      8.   SHARED DISPOSITIVE POWER
                    
    WITH            400,000 (see Item 4)
________________________________________________________________________________
9.   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     400,000 (see Item 4)

________________________________________________________________________________
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                                                          [_]

________________________________________________________________________________
11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

     1.8% (see Item 4)

________________________________________________________________________________
12.  TYPE OF REPORTING PERSON*

     00

________________________________________________________________________________
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                  Page 2 of 12




CUSIP No. 91307C102                   13G                    Page 3 of 12 Pages


________________________________________________________________________________
1.   NAME OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

     S.A.C. Capital Management, LLC

________________________________________________________________________________
2.   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                 (a)  [_]
                                                                 (b)  [X]

________________________________________________________________________________
3.   SEC USE ONLY



________________________________________________________________________________
4.   CITIZENSHIP OR PLACE OF ORGANIZATION

     Delaware

________________________________________________________________________________
  NUMBER OF    5.   SOLE VOTING POWER
                    
   SHARES           0
               _________________________________________________________________
BENEFICIALLY   6.   SHARED VOTING POWER
                    
  OWNED BY          400,000 (see Item 4)
               _________________________________________________________________
    EACH       7.   SOLE DISPOSITIVE POWER
                    
  REPORTING         0
               _________________________________________________________________
   PERSON      8.   SHARED DISPOSITIVE POWER
                    
    WITH            400,000 (see Item 4)
________________________________________________________________________________
9.   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     400,000 (see Item 4)

________________________________________________________________________________
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                                                          [_]

________________________________________________________________________________
11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

     1.8% (see Item 4)

________________________________________________________________________________
12.  TYPE OF REPORTING PERSON*

     00

________________________________________________________________________________
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                  Page 3 of 12





CUSIP No. 91307C102                   13G                    Page 4 of 12 Pages


________________________________________________________________________________
1.   NAME OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

     S.A.C. Capital Associates, LLC

________________________________________________________________________________
2.   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                 (a)  [_]
                                                                 (b)  [X]

________________________________________________________________________________
3.   SEC USE ONLY



________________________________________________________________________________
4.   CITIZENSHIP OR PLACE OF ORGANIZATION

     Anguilla, British West Indies

________________________________________________________________________________
  NUMBER OF    5.   SOLE VOTING POWER
                    
   SHARES           0
               _________________________________________________________________
BENEFICIALLY   6.   SHARED VOTING POWER
                    
  OWNED BY          400,000 (see Item 4)
               _________________________________________________________________
    EACH       7.   SOLE DISPOSITIVE POWER
                    
  REPORTING         0
               _________________________________________________________________
   PERSON      8.   SHARED DISPOSITIVE POWER
                    
    WITH            400,000 (see Item 4)
________________________________________________________________________________
9.   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     400,000 (see Item 4)

________________________________________________________________________________
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                                                          [_]

________________________________________________________________________________
11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

     1.8% (see Item 4)

________________________________________________________________________________
12.  TYPE OF REPORTING PERSON*

     00

________________________________________________________________________________
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                  Page 4 of 12





CUSIP No. 91307C102                   13G                    Page 5 of 12 Pages


________________________________________________________________________________
1.   NAME OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

     Sigma Capital Management, LLC

________________________________________________________________________________
2.   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                 (a)  [_]
                                                                 (b)  [X]

________________________________________________________________________________
3.   SEC USE ONLY



________________________________________________________________________________
4.   CITIZENSHIP OR PLACE OF ORGANIZATION

     Delaware

________________________________________________________________________________
  NUMBER OF    5.   SOLE VOTING POWER
                    
   SHARES           0
               _________________________________________________________________
BENEFICIALLY   6.   SHARED VOTING POWER
                    
  OWNED BY          1,466,826* (see Item 4)
               _________________________________________________________________
    EACH       7.   SOLE DISPOSITIVE POWER
                    
  REPORTING         0
               _________________________________________________________________
   PERSON      8.   SHARED DISPOSITIVE POWER
                    
    WITH            1,466,826* (see Item 4)
________________________________________________________________________________
9.   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,466,826* (see Item 4)

________________________________________________________________________________
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                                                          [_]

________________________________________________________________________________
11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

     6.6% (see Item 4)

________________________________________________________________________________
12.  TYPE OF REPORTING PERSON*

     00

________________________________________________________________________________
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                  Page 5 of 12





CUSIP No. 91307C102                   13G                    Page 6 of 12 Pages


________________________________________________________________________________
1.   NAME OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

     Sigma Capital Associates, LLC

________________________________________________________________________________
2.   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                 (a)  [_]
                                                                 (b)  [X]

________________________________________________________________________________
3.   SEC USE ONLY



________________________________________________________________________________
4.   CITIZENSHIP OR PLACE OF ORGANIZATION

     Anguilla, British West Indies

________________________________________________________________________________
  NUMBER OF    5.   SOLE VOTING POWER
                    
   SHARES           0
               _________________________________________________________________
BENEFICIALLY   6.   SHARED VOTING POWER
                    
  OWNED BY          1,466,826* (see Item 4)
               _________________________________________________________________
    EACH       7.   SOLE DISPOSITIVE POWER
                    
  REPORTING         0
               _________________________________________________________________
   PERSON      8.   SHARED DISPOSITIVE POWER
                    
    WITH            1,466,826* (see Item 4)
________________________________________________________________________________
9.   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,466,826* (see Item 4)

________________________________________________________________________________
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                                                          [_]

________________________________________________________________________________
11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

     6.6% (see Item 4)

________________________________________________________________________________
12.  TYPE OF REPORTING PERSON*

     00

________________________________________________________________________________
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                  Page 6 of 12





CUSIP No. 91307C102                   13G                    Page 7 of 12 Pages


________________________________________________________________________________
1.   NAME OF REPORTING PERSONS
     I.R.S. IDENTIFICATION NO. OF ABOVE PERSONS (ENTITIES ONLY)

     Steven A. Cohen

________________________________________________________________________________
2.   CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP*
                                                                 (a)  [_]
                                                                 (b)  [X]

________________________________________________________________________________
3.   SEC USE ONLY



________________________________________________________________________________
4.   CITIZENSHIP OR PLACE OF ORGANIZATION

     United States

________________________________________________________________________________
  NUMBER OF    5.   SOLE VOTING POWER
                    
   SHARES           0
               _________________________________________________________________
BENEFICIALLY   6.   SHARED VOTING POWER
                    
  OWNED BY          1,866,826* (see Item 4)
               _________________________________________________________________
    EACH       7.   SOLE DISPOSITIVE POWER
                    
  REPORTING         0
               _________________________________________________________________
   PERSON      8.   SHARED DISPOSITIVE POWER
                    
    WITH            1,866,826* (see Item 4)
________________________________________________________________________________
9.   AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON

     1,866,826* (see Item 4)

________________________________________________________________________________
10.  CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES*

                                                                          [_]

________________________________________________________________________________
11.  PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)

     8.4% (see Item 4)

________________________________________________________________________________
12.  TYPE OF REPORTING PERSON*

     IN

________________________________________________________________________________
                     *SEE INSTRUCTIONS BEFORE FILLING OUT!


                                  Page 7 of 12




ITEM 1(a)        NAME OF ISSUER:

                 United Therapeutics Corporation

ITEM 1(b)        ADDRESS OF ISSUER'S PRINCIPAL EXECUTIVE OFFICES:

                 1110 Spring Street
                 Silver Spring, ND  20910

ITEMS 2(a)       NAME OF PERSON FILING:

                 This statement is filed by: (i) S.A.C. Capital Advisors, LLC,
                 ("SAC Capital Advisors") with respect to shares of common
                 stock, par value $0.01 per share ("Shares") of the Issuer
                 beneficially owned by S.A.C. Capital Associates, LLC ("SAC
                 Capital Associates"); (ii) S.A.C. Capital Management, LLC,
                 ("SAC Capital Management") with respect to Shares beneficially
                 owned by SAC Capital Associates; (iii) SAC Capital Associates
                 with respect to Shares beneficially owned by it; (iv) Sigma
                 Capital Management, LLC ("Sigma Capital Management") with
                 respect to Shares beneficially owned by Sigma Capital
                 Associates, LLC ("Sigma Capital Associates"); (v) Sigma Capital
                 Associates with respect to Shares beneficially owned by it; and
                 (vi) Steven A. Cohen with respect to Shares beneficially owned
                 by SAC Capital Advisors, SAC Capital Management, SAC Capital
                 Associates, Sigma Capital Management and Sigma Capital
                 Associates.

ITEM 2(b)        ADDRESS OF PRINCIPAL BUSINESS OFFICE:

                 The address of the principal business office of (i) SAC Capital
                 Advisors and Mr. Cohen is 72 Cummings Point Road, Stamford,
                 Connecticut 06902, (ii) SAC Capital Management and Sigma
                 Capital Management is 540 Madison Avenue, New York, New York
                 10022, and (iii) SAC Capital Associates, and Sigma Capital
                 Associates is P.O. Box 58, Victoria House, The Valley,
                 Anguilla, British West Indies.

ITEM 2(c)        CITIZENSHIP:

                 SAC Capital Advisors, SAC Capital Management and Sigma Capital
                 Management are Delaware limited liability companies. SAC
                 Capital Associates, and Sigma Capital Associates are Anguillan
                 limited liability companies. Mr. Cohen is a United States
                 citizen.


                                  Page 8 of 12





ITEM 2(d)        TITLE OF CLASS OF SECURITIES:

                 Common Stock, par value $0.01 per share

ITEM 2(e)        CUSIP NUMBER:

                 91307C102

ITEM 3           Not Applicable

ITEM 4           OWNERSHIP:

                 The percentages used herein are calculated based upon the
                 Shares issued and outstanding as of November 1, 2004 as
                 reported on the Issuer's quarterly report on Form 10-Q filed
                 with the Securities and Exchange Commission by the Company for
                 the fiscal year ended December 31, 2004.

                 As of the close of business on December 31, 2004:

                 1. S.A.C. Capital Advisors, LLC
                 (a) Amount beneficially owned: 400,000
                 (b) Percent of class: 1.8%
                 (c)(i) Sole power to vote or direct the vote: -0-
                 (ii) Shared power to vote or direct the vote: 400,000
                 (iii) Sole power to dispose or direct the disposition: -0-
                 (iv) Shared power to dispose or direct the disposition: 400,000

                 2. S.A.C. Capital Management, LLC
                 (a) Amount beneficially owned: 400,000
                 (b) Percent of class: 1.8%
                 (c)(i) Sole power to vote or direct the vote: -0-
                 (ii) Shared power to vote or direct the vote: 400,000
                 (iii) Sole power to dispose or direct the disposition: -0-
                 (iv) Shared power to dispose or direct the disposition: 400,000

                 3. S.A.C. Capital Associates, LLC
                 (a) Amount beneficially owned: 400,000
                 (b) Percent of class: 1.8%
                 (c)(i) Sole power to vote or direct the vote: -0-
                 (ii) Shared power to vote or direct the vote: 400,000
                 (iii) Sole power to dispose or direct the disposition: -0-
                 (iv) Shared power to dispose or direct the disposition: 400,000


                                  Page 9 of 12



                 4. Sigma Capital Management, LLC
                 (a) Amount beneficially owned: 1,466,826*
                 (b) Percent of class: 6.6%
                 (c)(i) Sole power to vote or direct the vote: 1,466,826*
                 (ii) Shared power to vote or direct the vote: -0-
                 (iii) Sole power to dispose or direct the disposition: -0-
                 (iv) Shared power to dispose or direct the 
                 disposition: 1,466,826*

                 5. Sigma Capital Associates, LLC
                 (a) Amount beneficially owned: 1,466,826*
                 (b) Percent of class: 6.6%
                 (c)(i) Sole power to vote or direct the vote: -0-
                 (ii) Shared power to vote or direct the vote: 1,466,826*
                 (iii) Sole power to dispose or direct the disposition: -0-
                 (iv) Shared power to dispose or direct the
                 disposition: 1,466,826*

                 6. Steven A. Cohen
                 (a) Amount beneficially owned: 1,866,826*
                 (b) Percent of class: 8.4%
                 (c)(i) Sole power to vote or direct the vote: -0-
                 (ii) Shared power to vote or direct the vote: 1,866,826*
                 (iii) Sole power to dispose or direct the disposition: -0-
                 (iv) Shared power to dispose or direct the
                 disposition: 1,866,826*

                 * The number of shares reported herein includes options held by
                 Sigma Capital Associates on 225,000 Shares.

                 SAC Capital Advisors, SAC Capital Management, Sigma Capital
                 Management, and Mr. Cohen own directly no Shares. Pursuant to
                 investment agreements, each of SAC Capital Advisors and SAC
                 Capital Management share all investment and voting power with
                 respect to the securities held by SAC Capital Associates.
                 Pursuant to an investment management agreement, Sigma Capital
                 Management maintains investment and voting power with respect
                 to the securities held by Sigma Capital Associates. Mr. Cohen
                 controls each of SAC Capital Advisors, SAC Capital Management
                 and Sigma Capital Management. By reason of the provisions of
                 Rule 13d-3 of the Securities Exchange Act of 1934, as amended,
                 each of (i) SAC Capital Advisors, SAC Capital Management and
                 Mr. Cohen may be deemed to own beneficially 400,000 Shares
                 (constituting approximately 1.8% of the Shares outstanding) and
                 (ii) Sigma Capital Management and Mr. Cohen may be deemed to
                 own beneficially 1,466,826 shares (constituting approximately
                 6.6% of the Shares outstanding). Each of SAC Capital Advisors,
                 SAC Capital Management, Sigma Capital Management and Mr. Cohen
                 disclaim beneficial ownership of any of the securities covered
                 by this statement.


                                 Page 10 of 12




ITEM 5            OWNERSHIP OF FIVE PERCENT OR LESS OF A CLASS:

                 If this statement is being filed to report the fact that as of
                 the date hereof the reporting person has ceased to be the
                 beneficial owner of more than five percent of the class of
                 securities, check the following. |_|

ITEM 6           OWNERSHIP OF MORE THAN FIVE PERCENT ON BEHALF OF ANOTHER
                 PERSON:

                 Not Applicable

ITEM 7           IDENTIFICATION AND CLASSIFICATION OF THE SUBSIDIARY WHICH
                 ACQUIRED THE SECURITY BEING REPORTED ON BY THE PARENT HOLDING
                 COMPANY:

                 Not Applicable

ITEM 8           IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP:

                 Not Applicable

ITEM 9           NOTICE OF DISSOLUTION OF GROUP:

                 Not Applicable

ITEM 10          CERTIFICATION:

         By signing below the signatory certifies that, to the best of his
knowledge and belief, the securities referred to above were not acquired and are
not held for the purpose of or with the effect of changing or influencing the
control of the issuer of the securities and were not acquired and are not held
in connection with or as a participant in any transaction having that purpose or
effect.



                                 Page 11 of 12



                                    SIGNATURE

         After reasonable inquiry and to the best of my knowledge and belief, I
certify that the information set forth in this statement is true, complete and
correct.

Dated: February 14, 2005

S.A.C. CAPITAL ADVISORS, LLC


By: /s/ Peter Nussbaum
    -----------------------------------------
Name: Peter Nussbaum
Title: Authorized Person

S.A.C. CAPITAL MANAGEMENT, LLC


By: /s/ Peter Nussbaum
    -----------------------------------------
Name: Peter Nussbaum
Title: Authorized Person

S.A.C. CAPITAL ASSOCIATES, LLC


By: /s/ Peter Nussbaum
    -----------------------------------------
Name: Peter Nussbaum
Title: Authorized Person

SIGMA CAPITAL MANAGEMENT, LLC


By: /s/ Peter Nussbaum
    -----------------------------------------
Name: Peter Nussbaum
Title: Authorized Person

SIGMA CAPITAL ASSOCIATES, LLC


By: /s/ Peter Nussbaum
    -----------------------------------------
Name: Peter Nussbaum
Title: Authorized Person

STEVEN A. COHEN


By: /s/ Peter Nussbaum
    -----------------------------------------
Name: Peter Nussbaum
Title: Authorized Person


                                  Page 12 of 12