Amendment No. 1 to

Exhibit 4.2(b)

Amendment No. 1 to

Third Amended and Restated Investor Rights Agreement

THIS AMENDMENT NO. 1 to the Third Amended and Restated Investor Rights Agreement dated December 6, 2004 (this “Amendment”) amends the Third Amended and Restated Investor Rights Agreement dated May 12, 2004 (the “Future IRA”) by and among Targacept, Inc. (the “Company”) and the holders of shares of the Company’s Series C Convertible Preferred Stock, $0.001 par value per share (“Series C Stock”), Series B Convertible Preferred Stock, $0.001 par value per share (“Series B Stock”), or Series A Convertible Preferred Stock, $0.001 par value per share (“Series A Stock” and, together with the Series C Stock and Series B Stock, “Preferred Stock”) party thereto. Capitalized terms used herein and not otherwise defined shall have the meanings ascribed to them in the Future IRA.

R E C I T A L S:

WHEREAS, the Future IRA was entered into in contemplation of an initial public offering of the Company’s common stock in order to amend, effective as of the closing of such initial public offering, the Company’s Second Amended and Restated Investor Rights Agreement dated November 26, 2002, as amended (the “Current IRA”), which is currently in effect; and

WHEREAS, by its terms, the Future IRA will not become effective or affect the Current IRA unless and until the prospective initial public offering is completed and will not become effective at all if such initial public offering is not completed on or before December 31, 2004 (the “Trigger Date”); and

WHEREAS, Section 3 of the Future IRA provides that the Future IRA may be amended only with the prior written consent of the Company and the holders of a majority of the outstanding Series A Registrable Securities and Series B Registrable Securities and at least 65% of the outstanding Series C Registrable Securities (collectively, the “Required Investors”); and

WHEREAS, the prospective initial public offering may not be completed on or before the Trigger Date, and the Company and the undersigned holders of Preferred Stock, constituting the Required Investors, desire to amend the Future IRA as provided herein to extend the Trigger Date;

NOW, THEREFORE, the undersigned parties agree as follows:

1. Section 2.1(a) of the Future IRA is hereby amended by deleting the first sentence in its entirety and replacing it with the following:

“Subject to the other provisions of this Section 2.1, Section 2.8 and Section 2.9, if, at any time or from time to time following the Eligibility Date (but in no event prior to (x) six months after the effective date of the first registration of the Company’s securities on Form S-1 or (y) three months after the effective date of any other registration of the Company’s securities, other than registrations on Form S-4, Form S-8 or comparable or successor forms and other than registrations for the account of selling stockholders on Form S-3 or a comparable or successor form), the Company shall receive a written

request (specifying that it is being made pursuant to this Section 2.1) from (i) Holders of at least a majority of the Series A Registrable Securities and Series B Registrable Securities, considered together, or (ii) Holders of Series C Registrable Securities that the Company file a registration statement under the Act covering the registration for offer and sale of (A) in the case of clause (i) above, at least thirty percent (30%) of all Series A Registrable Securities and Series B Registrable Securities, considered together, or (B) in the case of clause (ii) above, at least (1) thirty percent (30%) of all Series C Registrable Securities or (2) a number of Series C Registrable Securities for which the total gross proceeds in a public offering reasonably expected to be received by the requesting Holders is at least $7,500,000, then the Company shall, within ten (10) business days notify in writing all other Holders of such request.”

2. Section 9 of the Future IRA is hereby amended by replacing “December 31, 2004” therein with “June 30, 2005.”

3. As expressly amended hereby, the Future IRA shall continue in full force and effect.

4. For the avoidance of doubt, as used in the Future IRA and the Current IRA, the term “Series C Stock” shall include, without limitation, shares of Series C Stock issued and sold pursuant to the Series C Convertible Preferred Stock Purchase Agreement entered into on or about the date hereof.

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IN WITNESS WHEREOF, this Amendment No. 1 to the Third Amended and Restated IRA is executed as of the day and year first above written.

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