The Walt Disney Co., in a move designed to bolster its corporate governance, said Thursday its board will amend its bylaws to require that directors step down from the board if they receive a withhold vote by a majority of shareholder votes cast.

Disney has had to endure scrutiny-and in some cases criticism-of its business practices amid a series of controversies, including how retiring CEO Michael Eisner ran the company to a $140 million severance payment to former President Michael Ovitz.

As part of the new rule, any director who receives a majority of withhold votes during the shareholder vote to elect directors must submit a letter of resignation to the board’s governance and nominating committee, which will then recommend to the full board that the resignation be accepted. By withholding votes, shareholders register their disapproval for a proposal.

The board also voted to amend its bylaws to generally prohibit without shareholder approval the company repurchasing any shares from Disney investors who own at least a 2 percent stake if the sale price is above market price.