Exhibit 10.1

AMENDMENT #1

TO THE CONSOLIDATED EDISON, INC.

Long Term Incentive Plan

Effective May 19, 2003

As amended and restated effective January 1, 2008

Effective July 1, 2010

Consolidated Edison, Inc.

Pursuant to the resolution adopted by the Board of Directors of Consolidated Edison, Inc., at a meeting duly held on February 18, 2010, the undersigned hereby approves effective July 1, 2010, the amendment set forth below to the Consolidated Edison, Inc. Long Term Incentive Plan, effective May 19, 2003, as amended and restated effective, January 1, 2008.

ARTICLE 7. STOCK UNIT GRANTS TO DIRECTOR PARTICIPANTS is amended as follows:

1. Section 7.3 Annual Grants is replaced in its entirety with the following:

Section 7.3 Annual Grants. Effective May 19, 2003, through May 15, 2005, each Director Participant will be granted 1,300 Stock Units on the first business day after each Annual Meeting. Effective May 16, 2005, through June 30, 2010, the number of Stock Units granted to each Director Participant be increased to 1,500. Effective July 1, 2010, each Director Participant will be granted annual Stock Units valued at $90,000 on the first business day after each Annual Meeting. The actual number of Stock Units granted will be based on the closing price of a Share of Common 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 on the day of the Annual Meeting. If no trading of Shares of Common Stock occurred on such date, the closing price of a Share of Common Stock in such System as reported for the preceding day on which sales of Shares of Common Stock traded shall be used. The amount determined will be rounded to the nearest whole Stock Unit.

If a Director Participant is first appointed as a member of the Board on or after May 19, 2003, but before May 16, 2005, and is appointed after the Annual Meetings, his or her first annual grant of Stock Units (rounded to the nearest one hundred Stock Units) will be determined by multiplying 1,300 by the result from dividing the number of months before the next Annual Meeting by twelve; provided that for the purpose of this calculation the numerator shall exclude the month in which the effective date of the Director’s appointment occurs and shall include the month in which the next Annual Meeting occurs. If a Director Participant is first appointed as a member of the Board on or after May 16, 2005, but before July 1, 2010, and is appointed after the Annual Meetings, his or her first annual grant of Stock Units (rounded to the nearest one hundred Stock Units) will be determined by multiplying 1,500 by the result from dividing the number of months before the next Annual Meeting by twelve; provided that for the purpose of this calculation the numerator shall exclude the month in which the effective date of the Director’s appointment occurs and shall include the month in which the next Annual Meeting occurs. If a Director Participant is first

appointed as a member of the Board on or after July 1, 2010, and is appointed after the Annual Meetings, his or her first annual grant of Stock Units will be determined by multiplying $90,000 by the result from dividing the number of months before the next Annual Meeting by twelve; provided that for the purpose of this calculation the numerator shall exclude the month in which the effective date of the Director’s appointment occurs and shall include the month in which the next Annual Meeting occurs. The actual number of Stock Units granted will be based on the closing price of a Share of Common 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 on the day before the Director was first appointed as a member of the Board and will be rounded to the nearest whole Stock Unit. If no trading of Shares of Common Stock occurred on such date, the closing price of a Share of Common Stock in such System as reported for the preceding day on which sales of Shares of Common Stock traded shall be used. The Board, upon recommendation of the Corporate Governance and Nominating Committee, may from time-to-time change the annual grant.

IN WITNESS WHEREOF, the undersigned has executed this instrument this      day of June, 2010.

Mary Adamo

Vice President – Human Resources

Consolidated Edison Company of New York, Inc.