Twin brothers Cameron and Tyler Winklevoss, who claim Mark Zuckerberg stole their idea for the social networking site Facebook, have abandoned legal attempts to renegotiate the original $65m settlement.
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The settlement was made up of $20m in cash with the balance in shares, now thought to be worth more than $100m.
The twins claim Zuckerberg defrauded them by overstating the value of the shares when negotiating the settlement and they should therefore have the opportunity to renegotiate.
In April, a US appeals court ruled that the Winklevoss brothers would have to be satisfied with the settlement they reached with Zuckerberg in 2008, but their lawyer said his clients would ask the full appeals court for a rehearing.
In a document filed with the US 9th Circuit Court of Appeals in San Francisco on 22 June 2011, they said they will not pursue the matter any longer.
The document says that "after careful consideration" they have decided not to appeal to the US Supreme Court to overturn the appeal court's ruling, according to US reports.
In April, the appeals court noted that the brothers were accompanied to the negotiations by a team of lawyers and their father, a former accounting professor and expert on stock valuation.
"At some point, litigation must come to an end. That point has now been reached," said chief judge Alex Kozinski, noting that the brothers had signed a release of all claims against Facebook in 2008.