Jeremy Bamber's convictions for murdering five of his relatives more than 25 years ago will not be referred to the Court of Appeal, officials have said.
The notorious inmate, serving a whole life term for the 1985 killings, has always protested his innocence and claims his schizophrenic sister Sheila Caffell shot her family before turning the gun on herself in a remote Essex farmhouse.
The Criminal Cases Review Commission said that despite a lengthy and complex investigation, it "has not identified any evidence or legal argument that it considers capable of raising a real possibility that the Court of Appeal would quash the convictions".
The Commission said this was its final decision in its longest-running case.
Giving its reasons in a 109-page statement, it said: "Matters of pure speculation or unsubstantiated allegation constitute neither new evidence nor new argument capable of giving rise to a real possibility that the Court of Appeal will quash a conviction. Neither can such a real possibility arise from the accumulation of multiple unsubstantiated allegations.
"The Commission is satisfied that nothing in the submissions made by and on behalf of Mr Bamber or any issues raised in the recent documentary can, either individually or cumulatively, give rise to a real possibility that the Court of Appeal would find any of Mr Bamber's convictions to be unsafe."
Mr Bamber, who has twice lost appeals against his conviction, was told of the decision in prison, the Commission confirmed.
Bamber, 51, who is being held in Full Sutton prison in York, has been behind bars for 25 years for shooting his wealthy adopted parents, June and Neville, his sister Ms Caffell and her six-year-old twin sons Daniel and Nicholas at their farmhouse in Tolleshunt D'Arcy, Essex, on August 7, 1985.
In a statement issued by Bamber's supporters, the convicted killer said: "I shall continue to campaign to prove my innocence in every way I can. I am very shocked and extremely disappointed.
"It is illogical that the fresh evidence presented to them regarding the sound moderator has not persuaded the commissioners that this material 'may have' affected the jury's decision had they been presented with it at trial."