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An Australian man who confessed to killing US mathematician Scott Johnson in 1988 has had his conviction overturned on appeal.

Scott White was sentenced to jail in May, 33 years after Mr Johnson's body was found at the base of cliffs in Sydney.

The death was ruled as suicide at the time, but his family have long believed it was a gay hate crime.

Mr White, who is cognitively impaired, maintains he did not kill Mr Johnson.

His lawyers successfully argued the 52-year-old's guilty plea was made when he was "confused" and "stressed".

Mr White - who was 18 at the time of the alleged murder at North Head in Manly - had surprised his legal team when he declared "I am guilty" during a pre-trial hearing in the New South Wales Supreme Court in January.

Within half an hour, he had signed a statement saying he didn't kill the 27-year-old and had made the plea because he was worried his ex-wife - who claimed he had confessed the killing to her - would "come after" him.

But the court rejected an attempt by Mr White's lawyers to withdraw the plea and he was sentenced to eight years and three months in jail.

On Friday, the NSW Appeal Court found that the application to withdraw the plea should be considered again, setting aside Mr White's conviction and sentence.

If the application is successful, Mr White may face a retrial.

Speaking outside court, the detective in charge of investigating Mr Johnson's death, Peter Yeomans, said the man's US-based family were "very disappointed" with the outcome.

Mr Johnson's brother Steve campaigned for decades for the case to be re-investigated and called the sentence in May a "relief".

The police force has previously apologised to the family for not investigating the case properly in the 1980s and failing to protect the gay community.

It is now estimated up to 80 gay men were murdered in Sydney around that period - with many pushed off cliffs.

While Justice Helen Wilson in May found there was not enough evidence to establish Mr Johnson's death was a gay hate crime, she determined that his sexuality had "fed [Mr White's] indifference to his victim's fate".