A new investigation into the World's End murders has been launched under double jeopardy legislation, the Crown Office has said.
In 2007 Angus Sinclair was cleared of raping and murdering Christine Eadie and Helen Scott in 1977.
The girls were last seen leaving the World's End bar in Edinburgh. The judge ruled there was not enough evidence for the jury to reach a verdict.
Sinclair could now stand trial again as Lothain and Borders Police have been instructed to carry out further investigation into the murders.
A Crown Office spokesman said: "Whilst it is not appropriate to comment or speculate on the live investigation into these murders, the public can be assured that where there is new, compelling evidence of guilt, the length of time since committal or acquittal should offer no protection.
"We are committed to using the powers under the new double jeopardy legislation. We hope that this commitment will give reassurance to the families of Helen Scott and Christine Eadie."
The Crown said officials have met with the girls' families and they are being kept informed of developments in the case.
The Double Jeopardy (Scotland) Act 2011 sets out conditions where accused can be retried for a crime they were previously acquitted of.
If new evidence emerges, or it is found that an acquitted person has admitted to committing the offence, or where the original trial was "tainted", possibly by witness intimidation, the case can be investigated again.
When the law was discussed in parliament, the case of the World's End murders was frequently highlighted as showing the need for a law change that would allow a suspect to be tried twice for the same crime.
The Crown Office said other cases are under review by Solicitor General Lesley Thomson QC, and they may be prosecuted again under the Double Jeopardy Act.
The Scottish Government said it cannot comment on individual cases, but recent changes to the law had been made "in the interests of justice".
A spokeswoman said: "As the Justice Secretary said at the time, people shouldn't be able to walk free from court and subsequently boast with impunity about their guilt, 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 re-run.
"Prosecutors should not have their hands tied, and the legislative changes we brought in will ensure that in such cases individuals cannot evade justice."