Twin brothers Tyler and Cameron Winklevoss have decided against appealing to the Supreme Court over a ruling upholding their $65m settlement with Facebook and its founder Mark Zuckerberg,

The decision of the Winklevoss brothers could mark the end of a long-running dispute between the brothers and the social networking company made famous by the Hollywood movie "The Social Network."

The twin brothers have accused Facebook founder Mark Zuckerberg of stealing their idea for Facebook. They say that they had hired Zuckerberg to code their ConnectU site in 2003 after which he stole the idea and founded Facebook.

In 2008, Facebook agreed to a settlement with the brothers but did not admit to their claims that Zuckerberg had stolen their idea. In the deal, the brothers received $20m in cash and $45m worth of stock valued at $36 per share in the deal.

The settlement is now worth more than $160m. In their fresh application, in April, seeking re-opening of the case, the brothers had alleged that they were misled about Facebook’s value when they agreed to the 2008 settlement. However, a federal court ruled in favour of Zuckerberg, denying the Winklevoss brothers to re-open the $65m legal settlement signed in 2008.

A week later, the twin brothers sought permission to make their case to the entire Ninth Circuit, which the court rejected, according to a report by Agence France-Presse.

In May, the brothers were denied the permission to make their case to the entire Ninth Circuit.

The lawyer of the twin brothers has not disclosed the reasons behind the decision.