The California State Teachers' Retirement System, the second-largest largest pension fund in the United States, wants Facebook Inc to expand its board of directors and diversify a panel that has no women.

We are disappointed that the Facebook board will not have any women members, CalSTRS corporate governance director Anne Sheehan wrote in a letter to Facebook founder and Chief Executive Mark Zuckerberg Tuesday. We believe that investors and the company would benefit from a larger, more diverse board.

CalSTRS, which managed $150 billion in assets on February 2, said it held Facebook stakes through its private equity investments and expects to be a common stock holder when the social media company goes public later this year.

Sheehan in the letter urged Facebook to add new board members before the initial public offering. CalSTRS officials told Reuters on Monday that it was planning to engage with Facebook over its corporate governance concerns.

Facebook officials could not be reached immediately for comment.

Facebook last week filed for a $5 billion IPO, a deal that would value the upstart social media company at about $100 billion. In addition to being one of the biggest IPOs ever, the deal is drawing fire from corporate governance circles.

Facebook, for example, set up a series of defenses against proxy battles and unwanted takeover attempts, according to its filing with the U.S. Securities and Exchange Commission.

Zuckerberg also would remain in complete control of the company for the foreseeable future, so much so that the 27-year-old Harvard University drop-out would even have the right to appoint his own successor before he dies.

CalSTRS, though, is taking aim at a board of directors with six members in addition to Zuckerberg, the board's chairman: Marc Andreessen, Erskine Bowles, James Breyer, Donald Graham, Reed Hastings and Peter Thiel.

(Reporting By Paritosh Bansal and Joseph A. Giannone; Editing by Richard Chang)