<PAGE>   1
                                                                      Exhibit 24

                                POWER OF ATTORNEY


           The undersigned hereby appoints Lawrence J. Toal and James E. Kelly
or either of the foregoing persons acting alone, each with the full power of
substitution, as his true and lawful attorney-in-fact and agent, for him and in
his name and place, to sign the name of the undersigned in the capacity or
capacities indicated below to the Annual Report of Dime Bancorp, Inc. on Form
10-K for the year ended December 31, 2000 and any and all amendments to such
Form 10-K and to file the same, with all exhibits thereto and other documents in
connection therewith, with all necessary or appropriate governmental or other
entities, including, but not limited to, the Securities and Exchange Commission
and the New York Stock Exchange, granting to such attorney-in-fact and agent
full power and authority to perform each act necessary to be done as fully to
all intents and purposes as he might do in person, hereby ratifying and
confirming all that such attorney-in-fact and agent may lawfully do or cause to
be done by virtue hereof.



         Signature                     Title                          Date

/s/ Lawrence J. Toal           Chief Executive Officer,          March 16, 2001
---------------------------    President, Chief Operating
Lawrence J. Toal               Officer and a Director
                               (Principal Executive Officer)




/s/ Anthony P. Terracciano     Chairman of the Board              March 16, 2001
---------------------------      and a Director
Anthony P. Terracciano


/s/ Derrick D. Cephas          A Director                         March 16, 2001
---------------------------
Derrick D. Cephas


/s/ Frederick C. Chen          A Director                         March 16, 2001
---------------------------
Frederick C. Chen


/s/ J. Barclay Collins II      A Director                         March 16, 2001
---------------------------
J. Barclay Collins II


/s/ Richard W. Dalrymple       A Director                         March 16, 2001
---------------------------
Richard W. Dalrymple


/s/ James F. Fulton            A Director                         March 16, 2001
---------------------------
James F. Fulton


/s/ Fred B. Koons              A Director                         March 16, 2001
---------------------------
Fred B. Koons


/s/ Virginia M. Kopp           A Director                         March 16, 2001
---------------------------
Virginia M. Kopp
<PAGE>   2
         Signature                     Title                          Date

/s/ James M. Large, Jr.        A Director                         March 16, 2001
---------------------------
James M. Large, Jr.


/s/ Margaret Osmer-McQuade     A Director                         March 16, 2001
---------------------------
Margaret Osmer-McQuade


/s/ John Morning               A Director                         March 16, 2001
---------------------------
John Morning


/s/ Howard H. Newman           A Director                         March 16, 2001
---------------------------
Howard H. Newman


/s/ Sally Hernandez-Pinero     A Director                         March 16, 2001
---------------------------
Sally Hernandez-Pinero


/s/ Eugene G. Schulz, Jr.      A Director                         March 16, 2001
---------------------------
Eugene G. Schulz, Jr.


/s/ Howard Smith               A Director                         March 16, 2001
---------------------------
Howard Smith


/s/ Norman R. Smith            A Director                         March 16, 2001
---------------------------
Norman R. Smith


/s/ Ira T. Wender              A Director                         March 16, 2001
---------------------------
Ira T. Wender