Facebook has failed in its latest bid to sue DLA Piper and other law firms for briefly representing a fugitive New York businessman accused of fraudulently claiming an ownership stake in the social networking giant.

In a one-page ruling on Tuesday, the New York Supreme Court Appellate Division, First Department denied Facebook's motion for reargument in its malicious prosecution and attorney deceit case against businessman Paul Ceglia's erstwhile lawyers.

Facebook targeted firms including DLA Piper, Milberg, New York-based Lippes Mathias Wexler Friedman and eight individual lawyers, alleging they contributed to Ceglia's alleged fraud.

The ruling is the latest turn in a long and twisting dispute that began more than a half decade ago, when Ceglia sued Facebook and founder Mark Zuckerberg over an old contract that he claimed entitled him to as much as 84% of the company.

DLA Piper, Milberg and Lippes Mathias had each represented Ceglia at various points in the contract case but each firm withdrew within months. All three firms had dropped out by the time a federal judge in Buffalo dismissed Ceglia's claims in March 2014, ruling that he had forged his supposed contract with Zuckerberg.

By then, Ceglia was already facing criminal fraud charges in connection with his alleged multibillion-dollar courtroom shakedown. In March 2015, he fled home confinement and disappeared along with his wife and two young children. Authorities now consider him a fugitive.

After Ceglia's contract suit collapsed, Facebook took aim at his former lawyers in New York state court in late 2014, bringing claims for malicious prosecution and for deceit. When a trial court judge refused to dismiss the case last May, it prompted a First Department appeal.

The case was argued in October, with Tibor Nagy of Dontzin Nagy & Fleissig representing DLA Piper. Gregory Joseph of Joseph Hage Aaronson, who represents Milberg, and Brown Rudnick's Sigmund Wissner-Gross, who represents Lippes Mathias, also argued at the First Department.

The state appeals court cleared the three law firms in late December, but Facebook was not ready to give up. In January, the company asked the First Department to reconsider the case.

On Tuesday (17 May), the appeals court denied that request without elaboration, leaving only a narrow path forward for Facebook and its lawyers.

If the social network wants to continue the case, it will have to convince the New York Court of Appeals that it merits further review – potentially by arguing that the case raises constitutional questions or an issue that has state-wide significance.

The company's outside legal team is led by Kevin Huff and Mark Hansen of Kellogg Huber Hansen Todd Evans & Figel, as well as Geoffrey Hazard Jr, a legal ethics expert and emeritus law professor at the University of California and University of Pennsylvania.

A Facebook spokeswoman declined to comment on Wednesday. Representatives for the three law firms named in Facebook's suit did not immediately respond to requests for comment.