Cameron and Tyler Winklevos accused Zuckerberg of stealing the idea for Facebook after being employed by the pair to write code for a site called Harvard Connection.
The brothers and ConnectU, the successor company to Harvard Connection they founded with partner Divya Narendra, filled a lawsuit against the hugely popular social networking site in September 2004.
However, Zuckerberg finally settled the long-running lawsuit in June 2008.
Details of the settlement were kept under wraps until disclosed in a newsletter by Quinn Emanuel Urquhart Oliver & Hedges, the firm which represented ConnectU in the lawsuit.
While Facebook says it considers the matter concluded, Cameron Winkelvoss told the BBC: "I think it is safe to say the chapter is not closed on the matter".
"It's our duty to stand for principles. We're willing to wait around and make sure that's what right has been made right," added Tyler Winkelvoss.
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