PRICING SUPPLEMENT NO. 4                                        Rule 424(b)(3)
DATED:  May 19, 2003+                                      File No. 333-104455
        May 20, 2003++
(To Prospectus dated April 24, 2003,
and Prospectus Supplement dated April 24, 2003)

                                 $10,227,293,162
                         THE BEAR STEARNS COMPANIES INC.
                           MEDIUM-TERM NOTES, SERIES B

Principal Amount: $178,500,000  Floating Rate Notes [x]  Book Entry Notes [x]

Original Issue Date: 5/23/2003  Fixed Rate Notes [ ]     Certificated Notes [ ]

Maturity Date: 5/23/2005        CUSIP#: 073928ZL0

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:  Quarterly

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

[x]  LIBOR Telerate

[ ]  Prime Rate

[ ]  CMT Rate

Initial Interest Rate: 1.42%             Interest Payment Period:  Quarterly

Index Maturity:  Three Months

Spread (plus or minus):  +0.15%


+  $60,000,000 was traded on May 19, 2003.
++ $118,500,000 was traded on May 20, 2003.

*  On the 23rd of each August, November, February and May prior to Maturity.
** On the 23rd of each August, November, February and May, including the
   maturity date.

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