The Scottish government has signalled its intention to change the centuries-old law which prevents someone being tried for an offence for a second time.
It followed the publication of a Scottish Law Commission report into double jeopardy.
The review recommended that any change in the law should not be imposed retrospectively.
This would prevent Angus Sinclair being charged again with the World's End murders in Edinburgh 30 years ago.
Justice Secretary Kenny MacAskill said change was "needed now", and revealed that the Scottish government planned to bring forward new legislation "at the earliest practicable opportunity".
The family of one of the World's End victims said they were "deeply disappointed" that the commission did not want any change in the law to be applied retrospectively.
The Scottish Law Commission has spent two years investigating the law on double jeopardy, which was changed in England and Wales in 2003. Since then, six cases have been returned to court, resulting in three convictions.
The commission had been asked by Mr MacAskill to consider whether the rule should be changed after convicted murderer Sinclair was cleared of killing teenagers Helen Scott and Christine Eadie, who were last seen leaving the World's End pub in Edinburgh in 1977.
Sinclair's trial collapsed in 2007 when judge Lord Clarke ruled that the Crown had insufficient evidence to proceed.
A change in the law which would allow retrials of people cleared of murder or rape has all-party support at Holyrood, and the commission has provided a draft bill for MSPs.
However, it said any new law should not be retrospective, even if there was significant new evidence.
Patrick Layden, QC, lead commissioner on the review, said he believed the basic principles behind double jeopardy should remain.
He said it was up to parliament to decide whether or not retrials could be held in serious cases where strong new evidence became available after the accused was acquitted.
Mr Layden added: "The rule against double jeopardy has protected the citizens of Scotland against repeated prosecutions for hundreds of years.
"Essentially, it prevents the state from running the criminal prosecution system on a 'Heads we win; tails, let's play again until you lose' basis. So we are recommending that it should be kept, and put into legislation."
But Mr Layden said there was a division of opinion within the commission on whether there should be a possibility of a retrial on the basis of new evidence.
He said: "It would not be right to allow the state, with its large resources, to try, try and try again to get a conviction.
"On the other hand, if there is genuinely new evidence, it is open to parliament to take the view that justice demands another trial."
If the Scottish Parliament does decide to introduce the possibility of retrial, the commission recommended that it should be confined to the most serious offences - rape or murder - but that ministers should be able to seek parliament's consent to add further offences in the future.
In a statement, Helen Scott's father Morain said: "It is of extreme importance that the victims of crime and the Scottish public have complete confidence in the ability of Scotland's criminal justice system to deliver justice.
"In our opinion today's recommendations by the Scottish Law Commission fall far short of meeting these expectations.
"We are in complete agreement that it would be wrong to be allowed to persecute people indefinitely but the law has to be fit for purpose, and with the advances in science and technology we find it hard to believe that it is recommended that any proposed changes should not be applied retrospectively."
He said it was now up to the Scottish Parliament to decide the final chapter of the World's End case, and added: "We hope that their decision is the right one".
Mr MacAskill said the Scottish government would consider the commission's recommendations carefully.
But he said: "There is a clear direction of travel and I want to ensure that Scotland has a double jeopardy law which is fit for the 21st Century.
"I believe that Scotland's approach to double jeopardy should reflect the interests of justice and not just the accused.
"We will now fully assess the Scottish Law Commission report before responding, but the intention is to legislate at the earliest practicable opportunity because change is needed and needed now."
Scottish Labour's justice spokesman Richard Baker said: "I am disappointed that the Law Commission have not recommended a change in the law. The failure of the prosecution of Angus Sinclair for his horrific crimes demonstrated the clear need to update the law in this area.
"Labour has been calling for a reform of double jeopardy for some time as the justice system needs to be rebalanced to take more account of the needs of victims of crime."
A BBC Scotland investigation has examined the crimes of Angus Sinclair and the question of whether he will ever stand trial again. Scotland's Secret Serial Killer will be shown on BBC2 at 2100 BST on Thursday 10 December.