Legislation that could let suspects who have escaped punishment face a retrial comes into force in Scotland on Monday.
The double jeopardy principle - which stops an acquitted suspect being tried again - will be enshrined in law, but exceptions will now be permitted.
A suspect could face retrial for a very serious crime if "compelling new evidence" has emerged.
A retrial could also be ordered where the original trial was tainted or a suspect has admitted the offence.
Justice Secretary Kenny MacAskill asked for a review of the double jeopardy principle in 2007 after convicted murderer Angus Sinclair was cleared of killing Helen Scott and Christine Eadie.
The teenagers were last seen leaving the World's End pub in Edinburgh in 1977.
A change in the law was backed by the Scottish Law Commission following a two-year investigation, though it recommended any changes should not be applied retrospectively.
The Double Jeopardy (Scotland) Act was passed unanimously by MSPs in March.
Mr MacAskill said the principle of double jeopardy had stood for 800 years, but the law had to be modernised to ensure it was fit for the 21st Century.
He said: "This is a victory for common sense. In this day and age, 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 these legislative changes will ensure that in such cases there will be no escape from justice."
Scottish Labour's justice spokeswoman Johann Lamont said the change was a "victory" for the victims of crime.
"When a family loses a loved one there can be no pain greater than knowing that their killer is still on the loose - something that is only compounded when a case is brought to trial and no conviction is secured.
"With the rapid advancement of technology and increasing sophistication of DNA evidence, police and law enforcement officials have more tools at their disposal to investigate past crimes than ever before.
"It is therefore absolutely right that we reform our laws to bring them into the 21st Century."
Under the new law, original trial evidence might be deemed "tainted" if witnesses had been intimidated.
The legislation also allows a suspect to face retrial on a more serious charge if the victim has died since the original trial.