The Winklevoss Twins, who sued Facebook founder Mark Zuckerberg for allegedly copying their idea for the world’s most popular social networking site, are now taking the fight to a federal court in Boston, a day after they decided not to appeal a U.S. Supreme Court to undo a 2008 settlement with Zuckerberg.

The twins and partner Divya Narendra filed a report in the U.S. District Court for the District of Massachusetts on Thursday asking a judge to investigate whether or not Facebook intentionally or inadvertently suppressed evidence during earlier litigation between the two parties.

On Wednesday, the Winklevosses and Narendra told a California court that they would not appeal a 2008 settlement they struck with Facebook and will accept their $65 million settlement. The trio filed papers with the U.S. Court of Appeals for the 9th Circuit in San Francisco saying that after careful consideration they had decided not to file a petition to take their case to the U.S. Supreme Court.

They had argued that the settlement should be thrown out because Facebook hadn't been honest about its own internal valuation at the time.

In April 2011, a federal appeals court ruled that former classmates of Facebook founder Mark Zuckerberg must abide by a deal they made when they fought Zuckerberg over ownership of the idea for a social networking site.

The 9th U.S. Circuit Court of Appeals said Cameron and Tyler Winklevoss were sophisticated enough to know what they were signing when they settled their original lawsuit in 2008. That settlement included a large cash payment of $65 million for the Winklevosses and Divya Narendra, their partner.

However, the Thursday filing has alternate legal grounds, although the goal is the same, namely to get more than their original 2008 $65 million settlement (in cash and private shares) from Facebook.

The argument for the Massachusetts case is that Facebook should have disclosed during the settlment the communications Mark Zuckerberg had with his associates back in 2003 and 2004 that pertained to the Winklevoss twins.

These conversations suggest that Zuckerberg intentionally delayed his work for the Winklevoss twins' social networking site, ConnectU, in order to launch Facebook first.

The original lawsuit was filed in 2004. The Winklevosses said Mark Zuckerberg, after promising to work on their social networking site, to be called HarvardConnection (later ConnectU), had essentially stolen the idea and some of the code, and broken an oral agreement. The dispute was famously portrayed in the Oscar nominated film The Social Network in 2010.