Grant Number

Exhibit 10.24

July 28, 2005

Mr. [Name of Director]

[Address of Director]

RE:    Pegasystems Inc. (the “Company”) Board Resolution dated April 6, 2005

Dear [Name of Director]:

As you may recall, at the Board of Directors meeting held on April 6, 2005, the Board approved an amendment to certain stock option agreements between the Company and each of Alexander d’Arbeloff, Richard Jones, Steven Kaplan, William Keough, Edward Maybury, James O’Halloran, Edward Roberts and William Wyman (each, a “Director Optionee”).

Pursuant to these amendments, the Company agreed to extend the period of time during which a Director Optionee may exercise the applicable stock option following the date upon which such Non-Employee Director ceased to be a member of the Company’s Board of Directors. The amendments provide that, if a Director Optionee has been a member of the Board of Directors for five years or more as of the date that such Non-Employee Director ceases to be a Board member, such Non-Employee Director may exercise the applicable stock option at any time before the scheduled expiration date of the option agreement (which is typically ten years from the date of grant).

These amendments apply to all grants of stock options held by a Director Optionee with an exercise price equal to or greater than the fair market value of the Company’s common stock on April 6, 2005. These amendments do not apply to any option grants held by a Director Optionee with an exercise price of less than the fair market value of the Company’s common stock on April 6, 2005. These terms also apply to all future option grants to Director Optionees.

In your case, the following Option Agreements are affected by the passage of this resolution by the Company’s Board of Directors:

This letter, once fully-signed, shall constitute a formal amendment to the Option Agreements listed above in order to affect the resolution adopted at the April 6, 2005 meeting. Accordingly, please provide us with your written acknowledgement of these amendments by executing one copy of this letter in the space below and returning it to my attention at the Company.

Please let me know if you have any questions.

Regards,

Acknowledged and Accepted: