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


                                  SCHEDULE 13G


                    UNDER THE SECURITIES EXCHANGE ACT OF 1934

                               (AMENDMENT NO. 3)*

                            FalconStor Software, Inc.
--------------------------------------------------------------------------------
                                (Name of Issuer)

                         Common Stock, $0.001 Par Value
--------------------------------------------------------------------------------
                         (Title of Class of Securities)

                                    306137100
                                 --------------
                                 (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 in 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 7



CUSIP No. 306137100                      13G
--------------------------------------------------------------------------------

1     NAMES OF REPORTING PERSONS
      I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

                                       Eli Oxenhorn

--------------------------------------------------------------------------------

2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                  (a) |_|

                                                                  (b) |_|

--------------------------------------------------------------------------------

3     SEC USE ONLY


--------------------------------------------------------------------------------

4     CITIZENSHIP OR PLACE OF ORGANIZATION

                                                                   United States
--------------------------------------------------------------------------------

                  5   SOLE VOTING POWER
                      2,898,932 shares
    Number of     --------------------------------------------------------------
      Shares
   Beneficially   6   SHARED VOTING POWER
     Owned By         241,077 shares
       Each       --------------------------------------------------------------
    Reporting
      Person      7   SOLE DISPOSITIVE POWER
       With           2,898,932 shares
                  --------------------------------------------------------------

                  8   SHARED DISPOSITIVE POWER
                      241,077 shares
--------------------------------------------------------------------------------

9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                                     3,140,009 shares

--------------------------------------------------------------------------------

10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES (SEE
      INSTRUCTIONS)
                                                                             |_|
--------------------------------------------------------------------------------

11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
                                           6.7%
--------------------------------------------------------------------------------

12    TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                                            IN

--------------------------------------------------------------------------------

                                  Page 2 of 7



CUSIP No. 306137100                      13G
--------------------------------------------------------------------------------

1     NAMES OF REPORTING PERSONS
      I.R.S. IDENTIFICATION NOS. OF ABOVE PERSONS (ENTITIES ONLY)

                         Eli Oxenhorn Family Limited Partnership

--------------------------------------------------------------------------------

2     CHECK THE APPROPRIATE BOX IF A MEMBER OF A GROUP (SEE INSTRUCTIONS)

                                                                  (a) |_|

                                                                  (b) |_|

--------------------------------------------------------------------------------

3     SEC USE ONLY


--------------------------------------------------------------------------------

4     CITIZENSHIP OR PLACE OF ORGANIZATION

                                                                        New York
--------------------------------------------------------------------------------


                  5   SOLE VOTING POWER
    Number of         241,077 shares
      Shares      --------------------------------------------------------------
   Beneficially
     Owned By     6   SHARED VOTING POWER
       Each           0 shares
    Reporting     --------------------------------------------------------------
      Person
       With       7   SOLE DISPOSITIVE POWER
                      241,077 shares
                  --------------------------------------------------------------

                  8   SHARED DISPOSITIVE POWER
                      0 shares
--------------------------------------------------------------------------------

9     AGGREGATE AMOUNT BENEFICIALLY OWNED BY EACH REPORTING PERSON
                                      241,077 shares

--------------------------------------------------------------------------------

10    CHECK BOX IF THE AGGREGATE AMOUNT IN ROW (9) EXCLUDES CERTAIN SHARES (SEE
      INSTRUCTIONS)
                                                                             |_|
--------------------------------------------------------------------------------

11    PERCENT OF CLASS REPRESENTED BY AMOUNT IN ROW (9)
                                           0.5%

--------------------------------------------------------------------------------

12    TYPE OF REPORTING PERSON (SEE INSTRUCTIONS)

                                            PN

--------------------------------------------------------------------------------

                                  Page 3 of 7



ITEM 1.

     (a)   Name of Issuer:
           FalconStor Software, Inc.

     (b)   Address of Issuer's Principal Executive Offices:
           2 Huntington Quadrangle
           Melville, NY 11747
ITEM 2.

1.   (a)   Name of Person Filing:       Eli Oxenhorn

     (b)   Address of Principal Business Office, or, if none, Residence:
                                        56 The Intervale
                                        Roslyn Estates, New York 11576
     (c)   Citizenship:                 United States

     (d)  Title of Class of Securities: Common Stock, $0.001 par value per share

     (e)  CUSIP Number:                 306137100

2.   (a)  Name of Person Filing:        Eli Oxenhorn Family Limited  Partnership

     (b)  Address of Principal Business Office, or, if none, Residence:
                                        56 The Intervale
                                        Roslyn Estates, New York 11576

     (c)  Place of Organization:        New York

     (d)  Title of Class of Securities: Common Stock, $0.001 par value per share

     (e)  CUSIP Number:                 306137100

ITEM 3.   If this statement is filed pursuant to ss.240.13d-1(b) or 240.13d-2(b)
          or (c), check whether the person is a:

     (a)  |_|  Broker or dealer registered under section 15 of the Act (15
               U.S.C.78o).

     (b)  |_|  Bank as defined in section 3(a)(6) of the Act (15 U.S.C. 78c).

     (c)  |_|  Insurance company as defined in section 3(a)(19) of the Act (15
               U.S.C. 78c).

     (d)  |_|  Investment company as registered under Section 8 of the
               Investment Company Act of 1940 (15 U.S.C. 80a-8).

     (e)  |_|  An investment adviser in accordance with
               ss.240.13d-1(b)(1)(ii)(E).

     (f)  |_|  An employee benefit plan or endowment fund in accordance with
               ss.240.13d-1(b)(1)(ii)(F).

     (g)  |_|  A parent holding company or control person in accordance with
               ss.240.13d-1(b)(1)(ii)(G).

     (h)  |_|  A savings associations as defined in Section 3(b) of the Federal
               Deposit Insurance Act (12 U.S.C. 1813).

     (i)  |_|  A church plan that is excluded from the definition of an
               investment company under section 3(c)(14) of the Investment
               Company Act of 1940 (15 U.S.C. 80a-3).

     (j)  |_|  Group, in accordance with ss.240.13d-1(b)(1)(ii)(J).

                                  Page 4 of 7



ITEM 4.     OWNERSHIP.

1.     Eli Oxenhorn:

              (a)    Amount Beneficially Owned: 3,140,009(1,2,3) shares.

              (b)    Percent of Class: 6.7%

              (c)    Number of shares as to which such person has:

                     (i)    sole power to vote or to direct the vote:
                            2,898,932(1) shares.

                     (ii)   shared power to vote or to direct the vote:
                            241,077(2,3) shares.

                     (iii)  sole power to dispose or to direct the disposition
                            of: 2,898,932(1) shares.

                     (iv)   shared power to dispose or to direct the disposition
                            of: 241,077(2,3) shares.

2.     Eli Oxenhorn Family Lmited Partnership:

              (a)    Amount Beneficially Owned: 241,077(2) shares. Eli Oxenhorn
                     is the general partner of the Eli Oxenhorn Family Limited
                     Partnership.

              (b)    Percent of Class: 0.5%

              (c)    Number of shares as to which such person has:

                     (i)    sole power to vote or to direct the vote: 241,077(2)
                            shares.

                     (ii)   shared power to vote or to direct the vote: 0
                            shares.

                     (iii)  sole power to dispose or to direct the disposition
                            of: 241,077(2) shares.

                     (iv)   shared power to dispose or to direct the disposition
                            of: 0 shares.

              Exhibit A, a Joint Filing Agreement, was previously filed with a
              Schedule 13G, dated August 22, 2001.

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. |_|

INSTRUCTION:  Dissolution of a group requires a response to this item.

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 OR
              CONTROL PERSON.

              Not Applicable.


----------
(1) Consists of 2,887,432 shares of Common Stock held by Mr. Oxenhorn, 3,500
shares held by the Eli Oxenhorn SEP IRA Account, and 8,000 shares held by the
Eli Oxenhorn Rollover IRA.

(2) Consists of 241,077 shares of Common Stock held by the Eli Oxenhorn Family
Limited Partnership.

(3) The reporting person disclaims beneficial ownership of these securities
except to the extent of his equity interest therein.


                                  Page 5 of 7



ITEM 8.       IDENTIFICATION AND CLASSIFICATION OF MEMBERS OF THE GROUP.

              Not Applicable.

ITEM 9.       NOTICE OF DISSOLUTION OF GROUP.

              Not Applicable.

ITEM 10.      CERTIFICATION.

              (b)    The following certification shall be included if the
                     statement is filed pursuant to ss.240.13d-1(c):

                     By signing below each party certifies that, to the best of
                     his/its 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 6 of 7



                                        SIGNATURE

      After  reasonable  inquiry and to the best of their  knowledge and belief,
each of the undersigned  hereby certifies that the information set forth in this
statement is true, complete and correct.

Dated:  January 5, 2005


                                    /s/ Eli Oxenhorn
                                       -----------------------------------------
                                        Eli Oxenhorn


                                    ELI OXENHORN FAMILY LIMITED PARTNERSHIP



                                    By:/s/ Eli Oxenhorn
                                       -----------------------------------------
                                       Name:  Eli Oxenhorn
                                       Title: General Partner

ATTENTION:  INTENTIONAL MISSTATEMENTS OR OMISSIONS OF FACT CONSTITUTE FEDERAL
            CRIMINAL VIOLATIONS (SEE 18 U.S.C. 1001)


                                  Page 7 of 7