PRICING SUPPLEMENT NO. 71                                         Rule 424(b)(3)
DATED: September 4, 2001                                      File No. 333-52902
(To Prospectus dated January 11, 2001,
and Prospectus Supplement dated January 11, 2001)


                                 $9,015,893,162
                         THE BEAR STEARNS COMPANIES INC.
                           MEDIUM-TERM NOTES, SERIES B


Principal Amount: $80,000,000   Floating Rate Notes [x]   Book Entry Notes   [x]

Original Issue Date: 9/12/2001  Fixed Rate Notes [ ]      Certificated Notes [ ]

Maturity Date:  12/12/2003      CUSIP#: 073928VE0

Option to Extend Maturity:      No   [x]
                                Yes  [ ]   Final Maturity Date:


                                             Optional         Optional
                       Redemption            Repayment        Repayment
  Redeemable On         Price(s)              Date(s)          Price(s)
  -------------      --------------       -------------      -----------
       N/A                 N/A                 N/A               N/A

Applicable Only to Fixed Rate Notes:
-----------------------------------

Interest Rate:

Interest Payment Dates:

Applicable Only to Floating Rate Notes:
--------------------------------------

Interest Rate Basis:                      Maximum Interest Rate: N/A

[ ]  Commercial Paper Rate                Minimum Interest Rate: N/A

[ ]  Federal Funds Effective Rate

[ ]  Federal Funds Open Rate              Interest Reset Date(s): *

[ ]  Treasury Rate                        Interest Reset Period: Monthly

[ ]  LIBOR Reuters                        Interest Payment Date(s): **

[x]  LIBOR Telerate

[ ]  Prime Rate

[ ]  CMT Rate

Initial Interest Rate: To be determined   Interest Payment Period:  Monthly
                       on 9/10/2001

Index Maturity:  One Month

Spread (plus or minus):  + 0.25%

*  On the 12th of each month prior to Maturity.

** On the 12th of each month, including the maturity date.

The distribution of Notes will conform to the requirements set forth in Rule
2720 of the NASD Conduct Rules.