Roadrunner may still have problems with Wile E. Coyote but Bugs Bunny is, for now, safe from Fox — 21st Century Fox that is.

Wednesday morning Time Warner, owner of Warner Bros., HBO, CNN and other major media channels, confirmed it had officially turned down Rupert Murdoch’s 21st Century Fox’s $80 billion offer to buy the company.

The bid, a cash-and-stock offer, that, according to the New York Times, was 60 percent in stock with the remainder in cash, would have broken down to $85 a share of Time Warner stock.

According to the statement made by Time Warner this morning, merging with 21st Century Fox is “not in the best interests of Time Warner or its stockholders to accept the Proposal or to pursue any discussions with 21st Century Fox.”

It is unclear what the next steps will be for 21st Century Fox, but Time Warner, an active player in some of the largest media mergers in the 1980s and the sale to America Online for $165 billion before the dot-com bubble burst, is for now remaining independent, though there are rumors that Google may be considering making a bid.

“It’s only a question of time until an Internet company buys a media company,” Laura Martin of Needham & Co, a growth-focused investment banking and asset-managing firm with headquarters in New York City, told Variety earlier this month.