AMENDMENT NO. 1 TO THE AGREEMENT AND PLAN OF MERGER

Exhibit 2.b

EXECUTION COPY

AMENDMENT NO. 1

TO THE

AGREEMENT AND PLAN OF MERGER

This AMENDMENT NO. 1 (this “Amendment”), dated as of July 11, 2005, to the Agreement and Plan of Merger, dated as of May 8, 2005 (the “Merger Agreement”), by and among Duke Energy Corporation, a North Carolina corporation (“Duke”), Cinergy Corp., a Delaware corporation (“Cinergy”), Duke Energy Holding Corp., a Delaware corporation (formerly Deer Holding Corp.) (the “Company”), Deer Acquisition Corp., a North Carolina corporation (“Merger Sub A”), and Cougar Acquisition Corp., a Delaware corporation (“Merger Sub B”).

WHEREAS, Section 7.03 of the Merger Agreement provides for the amendment of the Merger Agreement in accordance with the terms set forth therein; and

WHEREAS, the parties hereto desire to amend the Merger Agreement as set forth below;

NOW, THEREFORE, in consideration of the foregoing and the mutual covenants and agreements set forth herein and for good and valuable consideration, the receipt and adequacy of which is hereby acknowledged, and intending to be legally bound hereby, the parties hereto do hereby agree as follows:

ARTICLE I

DEFINITIONS

Section 1.1             Definitions; References.  Unless otherwise specifically defined herein, each term used herein shall have the meaning assigned to such term in the Merger Agreement.  Each reference to “hereof,” “herein,” “hereunder,” “hereby” and “this Agreement” shall, from and after the date hereof, refer to the Merger Agreement as amended by this Amendment.

ARTICLE II

AMENDMENTS TO MERGER AGREEMENT

Section 2.1             Amendments to Merger Agreement.  The Merger Agreement shall be amended as follows:

(a)           Section 2.02(b) of the Agreement is hereby amended by inserting the following sentence as the final sentence of the section:

“Notwithstanding anything to the contrary hereinbefore, subject to applicable law, the parties intend that the Company will implement a direct registration system at Closing, and if such direct registration system

is implemented by the Company at such time, all shares of Company Common Stock shall be in uncertificated book-entry form unless a physical certificate is requested by such holder.”

(b)           Section 2.02(e)(i) of the Agreement is hereby amended by inserting the following sentences as the final sentences of the section:

“Notwithstanding the foregoing, Duke and Cinergy shall use reasonable best efforts to cause the Duke Energy InvestorDirect Choice Plan (the “Duke DRIP”) and the Cinergy Corp. Direct Stock Purchase and Dividend Reinvestment Plan (the “Cinergy DRIP”) to be rolled over into a dividend reinvestment plan to be established and implemented by the Company on or prior to the Closing Date.  In connection with such roll-over, fractional shares of Company Common Stock will be issued to the participants in each of the Duke DRIP and the Cinergy DRIP in accordance with Section 2.01.”

(c)           Section 2.02(l) of the Agreement is hereby amending by inserting the following to the end of such section:

“provided, however, that Duke and Cinergy shall use reasonable best efforts so that uncertificated shares of Duke Common Stock held in the Duke DRIP and uncertificated shares of Cinergy Common Stock held in the Cinergy DRIP shall be exchanged for uncertificated shares of Company Common Stock in accordance with Section 2.01 and shall be held in a dividend reinvestment plan to be established and implemented by the Company on or prior to the Closing Date, in accordance with Section 2.02(e)(i).”

ARTICLE III

MISCELLANEOUS

Section 3.1             No Further Amendment.  Except as expressly amended hereby, the Merger Agreement is in all respects ratified and confirmed and all the terms, conditions, and provisions thereof shall remain in full force and effect.  This Amendment is limited precisely as written and shall not be deemed to be an amendment to any other term or condition of the Merger Agreement or any of the documents referred to therein.

Section 3.2             Effect of Amendment.  This Amendment shall form a part of the Merger Agreement for all purposes, and each party thereto and hereto shall be bound hereby.  From and after the execution of this Amendment by the parties hereto, any reference to the Merger Agreement shall be deemed a reference to the Merger Agreement as amended hereby.

Section 3.3             Governing Law.  This Amendment shall be governed by, and construed in accordance with, the laws of the State of New York, regardless of the laws that might otherwise govern under applicable principles of conflict of laws.

2

Section 3.4             Separability Clause.  In case any one or more of the provisions contained in this Amendment should be invalid, illegal or unenforceable in any respect, the validity, legality and enforceability of the remaining provisions contained herein shall not in any way be affected, impaired, prejudiced or disturbed thereby.

Section 3.5             Counterparts.  This Amendment may be simultaneously executed in several counterparts, and all such counterparts executed and delivered, each as an original, shall constitute one and the same instrument.

Section 3.6             Headings.  The descriptive headings of the several Articles of this Amendment were formulated, used and inserted in this Amendment for convenience only and shall not be deemed to affect the meaning or construction of any of the provisions hereof.

[Signature Page Follows]

3

IN WITNESS WHEREOF, Duke, Cinergy, the Company, Merger Sub A and Merger Sub B have caused this Agreement to be signed by their respective officers thereunto duly authorized, all as of the date first written above.

4