AMENDMENT TO THE BANKFINANCIAL CORPORATION

Exhibit 10.4

AMENDMENT TO THE

BANKFINANCIAL CORPORATION

2006 EQUITY INCENTIVE PLAN

NON-QUALIFIED STOCK OPTION AWARD TERMS

WHEREAS, BANKFINANCIAL Corporation (the “Company”) has granted non-qualified stock options to ROBERT J. O’SHAUGHNESSY (the “Participant”) pursuant to the certain Non-Qualified Stock Option Award Terms dated as of              involving              Covered Shares (the “Option”); and

WHEREAS, the Company and the Participant desire to amend certain provisions of the Option in order to provide that the Expiration Date be based on Termination of Employment following Participant’s attainment of age 70 rather than Participant’s Retirement.

NOW, THEREFORE, BE IT RESOLVED that, effective as of the 20th day of October, 2008, the Option is hereby amended in the following particulars:

1. Paragraph 4(a) of the Option is amended by deleting the existing language and replacing it with the following new Paragraph 4(a):

“(a) Notwithstanding the foregoing provisions of this Section 3, the Option shall become fully exercisable upon the earliest of the following events to occur: (i) a Change in Control that occurs on or before the Participant’s Termination of Service; (ii) the Participant’s Termination of Service as a result of the Participant’s Death or Disability; (iii) the Participant’s attainment of age 70; (iv) the Participant’s employment or consulting arrangement is terminated by the Company other than for Cause, or (v) the Participant terminates his employment for Good Reason (for purposes of this Agreement, the terms “Cause” and “Good Reason” shall have the meanings ascribed to them in the applicable employment agreement between the Participant and the Company or its Subsidiary.”

2. Paragraphs 5(c) and 5(d) of the Option are amended by deleting the existing language and replacing it with the following new Paragraphs 5(c), 5(d) and 5(e):

“(c) the twelve (12) month anniversary of the Participant’s Termination of Service if the Termination of Service occurs due to Death or Disability;”

(d) the twelve (12) month anniversary of the Participant’s Termination of Service if the Termination of Service occurs after the Participant’s attainment of age 70; or

(e) the three (3) month anniversary of the Participant’s Termination of Service if the Termination of Service occurs prior to the Participant’s attainment of age 70 for reasons other than

Death, Disability, or Cause; provided, however, that if the Participant returns to employment with, or as a director or consultant to, the Company, within three (3) months after the Termination of Service, such termination shall have no effect on the Option and the Participant shall have the same number of shares and the same vesting schedule as set forth in this Agreement.”

IN WITNESS WHEREOF, this Amendment has been executed as of the date first above written.

2