A British judge has cleared Bernard Madoff's sons of wrongdoing in a case brought against them by the liquidator of his estate in Britain, saying in a written ruling that the pair's honesty was not in doubt.

Judge Andrew Popplewell said Friday that the brothers, Mark and Andrew, were among several U.K. directors of Bernard Madoff's London-based securities firm whose reputations had been tainted by association with the elder Madoff's multibillion-dollar fraud.

The scheme unraveled in 2008 after Madoff confessed to his sons that his highly-regarded investment business was nothing more than a Ponzi scheme.

They reported him to the authorities, but some still suspect them of wrongdoing.

Popplewell dismissed allegations of impropriety against the brothers, saying in his judgment that their "integrity has been vindicated."