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                                                                  EXHIBIT 10.1.3

                               Amendment No. 1 to
                        Kevin Burke Employment Agreement

     The EMPLOYMENT AGREEMENT by and between Consolidated Edison, Inc, a New
York Corporation ("CEI), and Kevin Burke, dated as of September 1, 2000, is
amended effective May 31, 2002, as follows:

     WHEREAS, Kevin Burke (the "Executive") and Consolidated Edison, Inc.
entered into an Employment Agreement effective September 1, 2000 (the
"Agreement");

     WHEREAS, the parties to the Agreement desire to amend the Agreement to
provide for an additional grant of restricted stock units ("Units");

     NOW, THEREFORE, in consideration of the foregoing the parties hereto agree
as follows:

     1. The Agreement is amended to provide for an award (the "Additional
Restricted Stock Unit Award") of additional restricted stock units ("Additional
Units") with respect to 30,000 shares of the Common Shares ($.10 par value) of
CEI ("Stock"), effective as of May 31, 2002.

     2. The Additional Units shall vest in accordance with the following
schedule:

<Table>
<Caption>
                                              Percentage of Then Outstanding
            Date                               Non Vested Additional Units
            ----                               ---------------------------
         <S>                                           <C>
         08/31/2004                                     50%
         08/31/2005                                    100%
</Table>

     3. The cash value of a unit shall equal the closing price of a share of
                Stock in the Consolidated Reporting System as reported in the
                Wall Street Journal or in a similarly readily available public
                source for the trading day immediately prior to the applicable
                transaction date. If no trading of shares of Stock occurred on
                such date, the closing price of a share of Stock in such System
                as reported for the preceding day on which sales of shares of
                Stock occurred shall be used.

     4. (A) The Executive hereby elects to defer the receipt of any dividend
                equivalent cash payments that may become payable to the
                Executive on the Additional Units prior to December 31, 2003 and
                have the cash payment invested under the Company's Deferred
                Income Plan according to the terms and conditions of the
                Deferred Income Plan.

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        (B) Prior to the commencement of a calendar year, beginning with
calendar year 2004, the Executive shall have the right to elect to defer receipt
of any dividend equivalent cash payments that may become payable to the
Executive on the Additional Units in the calendar year and to have such cash
payments invested under the Company's Deferred Income Plan according to the
terms and conditions of the Deferred Income Plan.

     5. (A) Prior to the commencement of the calendar year in which the
Additional Units vest, the Executive may elect: (1) to defer the vesting of all
or a portion of the Additional Units, (2) to have, upon vesting, the cash value
of all or a portion of the Additional Units deferred and invested under the
Company's Deferred Income Plan according to the terms and conditions of the
Deferred Income Plan, or (3) any combination of the above listed options.

        (B) If no election is made, upon vesting, the cash value of the
Additional Units shall be automatically distributed to the Executive.

     6. All other terms and conditions of the initial Units as set forth in
Section 3(d) of the Agreement shall apply to the Additional Units.

     7. In all other respects, the Agreement remains in full force and effect.

     IN WITNESS WHEREOF, the Company has caused this Amendment to be executed by
its duly authorized officer and its corporate seal to be affixed hereto, and the
Executive has hereto set his hand as of the day and year first set forth above.

                                        CONSOLIDATED EDISON, INC.

                                        By:
                                           ------------------------
                                            Eugene R. McGrath
                           Chairman of the Board and Chief Executive Officer


                                           ------------------------
                                               Kevin Burke