Rewa is serving 22 years in prison for the rapes of Burdett and 24 other women.
Burdett was raped and bludgeoned to death in her Papatoetoe home in 1992.
As part of the homicide investigation swabs were taken from her body and semen was detected, but at the time the DNA found did not match anyone in the police databank.
In 1996 the DNA was then found to match that of Rewa and he was arrested and charged with Burdett's rape and murder on May 13 that year. He was also charged with sexual and violent offences against several other women.
However, by the time Rewa was arrested and charged, Teina Pora had already been convicted of the rape, murder and aggravated burglary of Burdett - with Pora's trial occurring in June 1994.
Rewa, nonetheless, stood trial on all charges from March to May in 1998. He was convicted of the sexual assaults but the jury failed to reach a verdict on the charges of rape and murder for Burdett.
A second trial was held in December 1998 on the Burdett charges alone and the jury convicted Rewa of rape but failed to reach a verdict on the murder charge.
On December 23, 1998 the Solicitor-General entered a stay of proceedings for a murder prosecution against Rewa.
Then in 2015, after a lengthy and public legal battle, the Privy Council quashed Pora's convictions for Burdett's rape and murder.
He had twice been convicted for the crime and spent 22 years in prison. He has since received an apology from the Government and $3.5 million compensation.
Last November the Deputy Solicitor-General, Brendan Horsley, on behalf of the Attorney-General, reversed the 1998 stay on the case, which appeared to clear the way for the third trial.
However, Chambers claimed the process was unlawful and the Attorney-General had no statutory or other power to lift the stay.
Chambers told the court there was also "no fresh evidence" to prosecute Rewa over the unsolved crime.
But in his decision, released this afternoon, Justice Venning said: "In the absence of any statutory provision restricting the Attorney-General's power, the common law power to lift the stay still exists. It remains unaffected.
"On its face the reversal of stay document sets out the grounds for the decision, namely that given the quashing of Mr Pora's convictions no one has been held accountable for a murder, and the evidential sufficiency supporting the murder charge against Mr Rewa.
"There is no evidence before the court of any bad faith on the part of the Attorney-General in relation to the decision to lift the stay. The fact the effect of lifting the stay is that Mr Rewa will face a third trial is not, of itself, sufficient to provide justification for the court to review the Attorney-General's decision. Third trials, although rare, have been held in certain cases."
A stay has never before been lifted in New Zealand.
The third trial is set to be heard in the High Court next February.
