Facebook's corporate governance rules, which give shareholders little say in how the social networking website would be run as a public company, are raising the hackles of one of the largest U.S. investors, the California State Teachers' Retirement System.

The pension fund, which has a portfolio valued at around $145 billion, is planning to send a letter to Facebook, hoping to engage the social networking website on corporate governance, two CalSTRS executives told Reuters in an interview on Monday.

We are in the beginning stages of talking to Facebook, said Janice Hester-Amey, a portfolio manager in CalSTRS Corporate Governance unit.

Facebook, which is run by Chief Executive and founder Mark Zuckerberg, declined to comment.

CalSTRS decided on Friday -- just two days after Facebook filed for a $5 billion initial public offering -- to try to talk to the website about improving its corporate governance.

CalSTRS invested in Facebook from its funds on the private equity side and is likely to invest in the company's publicly traded shares, Hester-Amey said.

No matter how brilliant you are, when you come to the public market -- not that we want to ever tell Zuckerberg or anyone like him how to run his company -- there should be some protection especially for long-term, patient money like CalSTRS, Hester-Amey said.

So I think there should be some more respect for capital, she said.

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

Under the governance provisions, Zuckerberg 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.

With a person that owns as much of the stock and the way he has set up the governance ... it will be very hard to influence him except if he's got some kind of a conscience, Hester-Amey said.

Facebook's corporate governance measures go against a decade-long trend of a move toward more shareholder-friendly corporate governance in the United States, prompted by institutional shareholders such as CalSTRS.

S&P 500 companies have been taking down classified boards, poison pills and other defenses over the years under pressure from institutional investors to have more shareholder-friendly governance rules.

For example, only about 24 percent of S&P 500 companies now have classified boards -- where only some of the directors come up for election every year -- down from 61 percent in 2002, according to FactSet SharkRepellent.

Facebook has two different classes of common stock, with Class B shares entitled to 10 votes per share against one vote per share for Class A. Class A stock is being sold to the public.

Zuckerberg has also struck voting agreements with investors including DST Global Ltd and Accel Partners. Overall he will have majority control after the IPO, giving him the power to determine the outcome of matters submitted to shareholders for approval, including the election of directors and any merger.

Given Zuckerberg's holdings, Facebook is also deemed a controlled company, which gives the company the right to not have an independent nominating committee of the board to choose directors.

Moreover, Facebook's governance rules say that when Class B shareholders have less than the majority of the combined voting power, the board will become staggered, only the board will be able to fill director vacancies and it will take a supermajority to change the company's by-laws.

Corporate governance expert Charles Elson said provisions such as the dual-class stock structure, different voting powers and Zuckerberg's ability to designate his successor were all reasons for concern.

I find it very troubling, said Elson, who is the director of John L. Weinberg Center for Corporate Governance at the University of Delaware. The whole tone to me was contrary to where governance has been moving, and the lessons that we have learned.

(Reporting By Paritosh Bansal)

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