PRICING SUPPLEMENT NO. 43                                       Rule 424(b)(3)
DATED: May 8, 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: $25,000,000   Floating Rate Notes [ ]  Book Entry Notes [x]

Original Issue Date: 5/25/2001  Fixed Rate Notes [x]     Certificated Notes [ ]

Maturity Date: 5/25/2016        CUSIP#: 073928UA9

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

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

Interest Rate: 7.00%

Interest Payment Dates: **

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

Interest Rate Basis:                     Maximum Interest Rate:

[ ]   Commercial Paper Rate              Minimum Interest Rate:

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

[ ]   Treasury Rate                      Interest Reset Period:

[ ]   LIBOR Reuters                      Interest Payment Date(s):

[ ]   LIBOR Telerate

[ ]   Prime Rate

[ ]   CMT Rate

Initial Interest Rate:                   Interest Payment Period:

Index Maturity:

Spread (plus or minus):

*     Commencing May 25, 2004 and on the interest payment dates thereafter until
      Maturity, the Notes may be called in whole at par at the option of the
      Company on ten calendar days notice.

**    Commencing November 25, 2001 and on the 25th of each May and November
      thereafter until Maturity or until the Notes are called.

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