Tyler and Cameron Winklevoss and a partner have filed a new motion in U.S. district court in Massachusetts, asking the court to determine whether Facebook and Zuckerberg intentionally or inadvertently suppressed evidence.
The twins accuse Zuckerberg of stealing their idea to create the social network.
On Wednesday, they dropped a similar case they were pursuing in the Ninth U.S. Circuit Court of Appeals.
There was no comment from Facebook on this latest court action.