UPDATE 2-Barnes & Noble won't let Burkle double his stake

* Rejects Burkle request to waive anti-takeover provision

* Riggio family, other insiders own 31 pct of shares

* Stock up 3.5 percent

CHICAGO, Feb 17 (Reuters) - Barnes & Noble Inc BKS.N said on Wednesday that it would not waive its poison pill anti-takeover provision to allow billionaire investor Ronald Burkle to nearly double his stake.

Barnes & Noble, the top brick-and-mortar U.S. bookstore chain, in a letter dismissed Burkle’s request, as well as complaints about the company’s corporate governance policies.

“The board has determined by unanimous vote that acceding to your request would not be in the best interests of all Barnes & Noble’s shareholders,” the company said in the letter, submitted in a U.S. Securities and Exchange Commission filing.

Officials at Burkle’s Yucaipa Cos LLC could not be reached for comment.

Barnes & Noble has been struggling with falling sales as more book-buying, including purchases of digital books for electronic readers, migrates online to companies such as Inc AMZN.O. Last month, Barnes & Noble said sales at its stores open at least a year fell 5.4 percent in December.

Burkle’s Yucaipa sent a letter to the company’s board on Jan. 28, seeking permission to raise its stake to up to 37 percent without tripping the pill’s provisions, which take effect once any investor tops 20 percent ownership.

Yucaipa bought 500,000 Barnes & Noble shares in January, raising its stake to 18.7 percent from 17.8 percent. It had earlier bought 5.7 million shares in quick succession in October and November, prompting Barnes & Noble’s board, led by Chairman Leonard Riggio, to pass the poison pill in November.

A 37 percent stake would make Yucaipa the chain’s largest shareholder, ahead of Riggio, who founded the company with a single bookstore in 1965.

The retailer’s poison pill is designed to prevent hostile takeovers by allowing current shareholders to dilute a raider’s holdings by purchasing more shares at a discount. It also allows existing Barnes & Noble shareholders to purchase a buyer’s shares at a steep discount in case of a takeover.

In Burkle’s January letter, he reiterated concerns about Barnes & Noble’s corporate governance policies and enforcement, complaining that insiders, including the Riggio family, may not be held to the same poison pill rules.

The company said in its letter on Wednesday that the Riggio family and other insiders held about 31 percent of its shares, excluding options that are not votable.

Burkle also asked the board to confirm that members of the Riggio family cannot collectively or individually buy any more shares without triggering the poison pill.

Barnes & Noble shares rose 75 cents, or 3.5 percent, to $21.95 in morning trading on the New York Stock Exchange. (Reporting by Ben Klayman; Editing by Lisa Von Ahn)