A judge threw out a second lawsuit filed by the Winklevoss twins late last week, with the Olympic rowers failing to plump up an earlier $65m settlement with the social network and its founder Mark Zuckerberg.
Cameron and Tyler Winklevoss, alongside business partner Divya Narendra, launched another attack on Zuck's social empire in June, immediately after the men ended a Supreme Court appeal against an earlier ruling.
They had tried to convince a judge to investigate whether Facebook had "intentionally or inadvertently suppressed evidence".
In June, the Winklevoss bros and Narendra backed away from an appeal against a ruling upholding their $65m settlement with Facebook that followed a long-running dispute with Zuckerberg.
Earlier this year the three men, whose lawsuits were brought by their company ConnectU Inc, lost an appeal against a February 2008 settlement with Facebook, which granted them $20m in cash and $45m in the firm's shares.
That same month, the twins and Narendra planned to ask the Boston federal court to look into their allegations that Facebook and the company's legal team concealed instant messages from them during litigation.
On Friday, Reuters reports that Boston-based US District Judge Douglas Woodlock rejected litigation over the accord.
The judge ruled that Facebook had successfully argued that the claims made by the founders of ConnectU had already been dismissed by the courts. ®