<PAGE>   1
                                                                   Exhibit 10.45

                                                 Amendment to the
                                                Dime Bancorp, Inc.
                                           Senior Officer Incentive Plan


                  Effective as of January 1, 2000, the Dime Bancorp, Inc. Senior
Officer Incentive Plan (the "Plan") is amended in the following particulars:

                  Section 2(e) of the Plan is hereby amended by adding at the
end of the last paragraph thereof the following new sentence to read as follows:

                  "Notwithstanding anything in this Plan to the contrary, none
                  of the execution of the Agreement and Plan of Merger, dated
                  September 15, 1999 and as amended and restated on December 27,
                  1999, between Hudson United Bancorp and the Company (the
                  'Merger Agreement'), the consummation of the merger of Hudson
                  United Bancorp with and into the Company, or the consummation
                  of the other actions or transactions contemplated by the
                  Merger Agreement, shall constitute a Change in Control under
                  the Plan."
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                                Amendment to the
                               Dime Bancorp, Inc.
                        Middle Management Incentive Plan


                  Effective as of January 1, 2000, the Dime Bancorp, Inc. Middle
Management Incentive Plan (the "Plan") is amended in the following particulars:

                  Section 8(b) of the Plan is hereby amended by adding at the
end of the last paragraph thereof the following new sentence to read as follows:

                  "Notwithstanding anything in this Plan to the contrary, none
                  of the execution of the Agreement and Plan of Merger, dated
                  September 15, 1999 and as amended and restated on December 27,
                  1999, between Hudson United Bancorp and the Company (the
                  'Merger Agreement'), the consummation of the merger of Hudson
                  United Bancorp with and into the Company, or the consummation
                  of the other actions or transactions contemplated by the
                  Merger Agreement, shall constitute a Change in Control under
                  the Plan."
<PAGE>   3
                                Amendment to the
                               Dime Bancorp, Inc.
                        Senior Management Incentive Plan


                  Effective as of January 1, 2000, the Dime Bancorp, Inc. Senior
Management Incentive Plan (the "Plan") is amended in the following particulars:

                  Section 8(b) of the Plan is hereby amended by adding at the
end of the last paragraph thereof the following new sentence to read as follows:

                  "Notwithstanding anything in this Plan to the contrary, none
                  of the execution of the Agreement and Plan of Merger, dated
                  September 15, 1999 and as amended and restated on December 27,
                  1999, between Hudson United Bancorp and the Company (the
                  'Merger Agreement'), the consummation of the merger of Hudson
                  United Bancorp with and into the Company, or the consummation
                  of the other actions or transactions contemplated by the
                  Merger Agreement, shall constitute a Change in Control under
                  the Plan."