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The pair had threatened to go to US Supreme Court to overturn the decision but have now said they will not pursue it.
They offered no statement on what had prompted their decision to abandon the suit.
And Cameron and Tyler Winklevoss are not finished with Facebook yet. The dramatic seven-year legal feud that inspired "The Social Network" may have one last plot twist.
The Olympic rowers are pressing their case in federal court in Boston that Facebook did not turn over important information during litigation.
The Winklevosses are not the first parties bested by a competitor who then seek to gain through litigation what they were unable to achieve in the marketplace.
