AMENDMENT NUMBER TWO TO EXCLUSIVE LICENSE AGREEMENT BETWEEN THE REGENTSOF THE UNIVERSITY OF CALIFORNIA AND NEUROGESX, INC.

Exhibit 10.6.2

AMENDMENT NUMBER TWO

TO

EXCLUSIVE LICENSE AGREEMENT

BETWEEN

THE REGENTS OF THE UNIVERSITY OF CALIFORNIA AND NEUROGESX, INC.

This Amendment Number Two is made effective December 2, 2003 (the “Amendment Date”) between THE REGENTS OF THE UNIVERSITY OF CALIFORNIA, a California corporation having its statewide administrative offices at 1111 Franklin Street, Oakland, California ###-###-####, (“The Regents”), and acting through its Office of Technology Management, University of California San Francisco, 185 Berry Street, Suite 4603, San Francisco, CA 94107 (“UCSF”) and NEUROGESX, INC., a California corporation having a principal place of business at 981F Industrial Boulevard, San Carlos, California, (the “Licensee”) (together “the Parties”). The Parties hereby amend that certain Exclusive License Agreement, dated as of November 1, 2000 (the “Agreement”) and Amendment Number One dated as of November 1, 2001 (“Amendment One”).

WITNESSETH

WHEREAS, The Regents and Licensee entered into the Agreement and Amendment One;

NOW, THEREFORE, in and for consideration of the promises and covenants contained herein and pursuant to Section 30.3 of the Agreement, The Regents and Licensee agree to amend the Agreement as follows:

1. Section 26.1 is hereby deleted in its entirety

SIGNATURES AND AGREEMENT

THIS AMENDMENT NUMBER TWO, AMENDMENT NUMBER ONE, AND THE EXCLUSIVE LICENSE AGREEMENT AS AMENDED BY THIS AMENDMENT NUMBER TWO AND AMENDMENT NUMBER ONE SETS FORTH THE ENTIRE AGREEMENT AND UNDERSTANDING OF THE REGENTS AND LICENSEE WITH RESPECT TO THE SUBJECT MATTER HEREOF, AND SUPERCEDES ALL PRIOR DISCUSSIONS, AGREEMENTS AND WRITINGS IN RELATION THERETO. ALL MATERIAL REPRESENTATIONS AND WARRANTIES ON WHICH THE PARTIES HAVE RELIED IN CONNECTION WITH THE NEGOTIATION OF THIS AMENDMENT, IF ANY, ARE STATED EXPRESSLY IN THIS AMENDMENT.

Except as stated in this Amendment Number Two, all other elements of the original Agreement, as previously amended, remain unchanged. In the event of any conflict between the terms of this Amendment Number Two and the License, the terms of this Amendment Number Two shall prevail.

This Amendment may be executed in counterparts, each of which shall be deemed an original, but both of which together shall constitute one and the same instrument.

IN WITNESS WHEREOF, the parties hereto have caused their duly authorized representatives to execute this Amendment.