The Crown has preserved forensic evidence from Sinclair's trial in 2007
Plans to reform the double jeopardy law in Scotland have been announced by Justice Secretary Kenny MacAskill.
The law, which prevents a person being tried twice for the same crime, is more than 800 years old, but was abolished in England and Wales five years ago.
The Scottish government is to hold a consultation on whether to permit retrials if new evidence emerges.
The proposal could see convicted killer Angus Sinclair stand trial over the World's End murders for a second time.
It will also consider the possibility of retrials in cases which were tainted by corruption or threats, or where the accused admitted the offence after being acquitted.
Mr MacAskill said his Government was minded to legislate "at the earliest opportunity".
"In this day and age, it should not be possible to walk free from court and subsequently boast with impunity about your guilt," he said.
Mr MacAskill has said the World's End case "scarred the soul of Scotland"
"If new evidence emerges which shows the original ruling was fundamentally flawed, it should be possible to have a second trial. And trials which are tainted by threats or corruption should be rerun.
"Prosecutors should not have their hands tied if there is new evidence or if someone admits to carrying out an offence years down the line.
"I believe any future changes should also be retrospective so that they extend to old cases."
The minister indicated four months ago that the law needed to be overhauled in response to recommendations by the Scottish Law Commission (SLC) that it be clarified.
However, his plans would go against the commission's report, which said any change to the law should not be applied to cases retrospectively.
The consultation, which runs from 22 March to 14 June, will seek the views of victims' families and the legal profession as well as other parties.
Mr MacAskill said: "With such a complex and important issue, it is absolutely imperative that we take the time to get it right to ensure that any law does not fall short of what is desired.
"This consultation is, therefore, an important stage of this journey and will allow us to get the views of those on the frontline, as well as those with a general interest."
The case of the unsolved World's End murders is frequently highlighted as showing the need for a law change.
Three years ago double killer Angus Sinclair, 62, was cleared of raping and murdering Christine Eadie and Helen Scott in 1977.
The charges were thrown out after the judge upheld a defence argument of insufficient evidence, although police and relatives of Ms Scott and Ms Eadie remain convinced of his guilt.
The plans to reform the law are supported by both Labour and the Conservatives.
Scottish Labour's justice spokesman Richard Baker said the justice system needed to be "rebalanced to take more account of the needs of victims of crime".
"We will scrutinise the detail of the Scottish government's proposals, but the experience of the reforms in England and Wales suggest that reforming the law in this area is a fair and proportionate measure," he added.
The Conservatives said it had been calling for this change since 2007.
Bill Aitken, the party's justice spokesman said: "In recent years, forensic technology has advanced to such an extent that material not previously useable as evidence could now be pivotal.
"In those few cases where new and compelling evidence could convict a criminal who committed a serious crime and deliver justice to families or victims, it is a change well worth making."