FIRST AMENDMENT TO THE TERADATA CORPORATION EMPLOYEE STOCK PURCHASE PLAN

Exhibit 10.7

FIRST AMENDMENT

TO THE TERADATA CORPORATION EMPLOYEE STOCK PURCHASE PLAN

AMENDMENT TO THE TERADATA CORPORATION EMPLOYEE STOCK PURCHASE PLAN (the “Plan”) as adopted and in effect October 1, 2007 by Teradata Corporation (“Teradata”).

WHEREAS, the Plan was adopted effective October 1, 2007; and

WHEREAS, Teradata desires to amend the Plan to allow greater flexibility in determining the period in which eligible employees may become participants under the Plan;

WHEREAS, Teradata desires to permit the Vice President, Human Resources, to have the authority to determine such periods pursuant to the authority granted to such executive officer under the terms of the Plan;

NOW, THEREFORE, Teradata does hereby amend the Plan, effective as of August 1, 2008, as follows:

Section 5 of the Plan is hereby amended in its entirety to read as follows:

Any Eligible Employee may become a Participant in the Plan by filing a stock purchase agreement (a “Stock Purchase Agreement”) in accordance with procedures established by the Vice President, Human Resources. Once an Eligible Employee has filed a Stock Purchase Agreement and become a Participant in the Plan, he shall remain a Participant until he withdraws from the Plan in accordance with Section 13 hereof, and he shall not be required to file a Stock Purchase Agreement for any succeeding Offering or Plan Year until he withdraws from the Plan.

A Participant may change his level of payroll deduction in accordance with procedures established by the Vice President, Human Resources.

IN WITNESS WHEREOF, Teradata has caused this amendment to the Plan to be executed this 29^th day of July, 2008.