Jeremy Bamber's convictions for murdering five of his relatives in Essex 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 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."
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 on August 7, 1985.
He was given a whole life tariff after being convicted of the murders in October 1986. In 2009 Bamber lost a Court of Appeal challenge against the order that he must die behind bars. He has twice lost appeals against conviction.
Bamber's lawyer Simon McKay said his client was "very disappointed" and considering applying for a judicial review of the Commission's decision.