Cameron and Tyler Winklevoss, along with partner Divya Narendra, have one last card to play in their legal battle with Facebook.

The twins' attorneys announced yesterday that they intend to file a petition with the U.S. Supreme Court, asking the high court to hear their case against Facebook and co-founder Mark Zuckerberg.

The petition stems from a settlement the Winklevosses and Narendra signed with the world's largest social network in 2008 after claiming Zuckerberg stole their idea for a social-networking site they called ConnectU. At that time, they were awarded $65 million from Facebook and Zuckerberg in exchange for dropping all further litigation against the site.

After the settlement was reached, the Winklevosses and Narendra said that the $65 million was based on a valuation of Facebook that was inaccurate. Facebook, which is now worth more than $50 billion, denied the claims, saying that the Winklevosses and Narendra received their fair share.

Last month, U.S. Ninth Circuit Court Judge Alex Kozinski shot down the Winklevoss' case, saying that the settlement they reached in 2008 was still binding.

"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," the chief judge wrote in the ruling. "And the courts might have obliged, had the Winklevosses not settled their dispute and signed a release of all claims against Facebook."

The Winklevoss' lead appellate attorney, Jerome B. Falk Jr., said his clients disagree. In a statement yesterday announcing his clients' plans to take their case to the U.S. Supreme Court, Falk said there is "a conflict between Ninth Circuit precedent and the decisions of other federal courts." Falk added that his clients believe they were "defrauded into entering into a settlement agreement."

"Settlements should be based on honest dealing, and courts have wisely refused to enforce a settlement obtained by fraudulent means," Falk said. "The court's decision shut the courthouse door to a solid claim that Facebook obtained this settlement by committing securities fraud. Our petition to the Supreme Court will ask the high court to decide whether that door should be reopened."

Whether the case will be reopened, however, remains to be seen. The high court must decide whether it will actually hear the case. And if it won't, the Winklevosses and Narendra may finally be forced to move on--something that Kozinski thought should have happened by now.

"At some point, litigation must come to an end," the judge said in last month's ruling. "That point has now been reached."

Facebook did not immediately respond to CNET's request for comment.