PRICING SUPPLEMENT NO. 45                                        Rule 424(b)(3)
DATED: May 15, 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: $15,000,000   Floating Rate Notes [ ]  Book Entry Notes [x]

Original Issue Date: 5/18/2001  Fixed Rate Notes [x]     Certificated Notes [ ]

Maturity Date: 5/17/2002        CUSIP#: 073928UC5

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: 4.350%

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):

*    On November 17, 2001 and at Maturity.

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