The police will not reinvestigate serial rapist Malcolm Rewa for the 1992 murder of Susan Burdett.
But new information received will be assessed, the Commissioner of Police, Mike Bush, told the Weekend Herald.
"No unresolved case is ever closed. As is normal for any historic inquiry, any new information ... will be assessed to determine what, if any further steps are required," Mr Bush said.
Tim McKinnel, the private investigator whose work led to the quashing, in March, of Teina Pora's convictions for rape and murder, said Mr Teina's support team were eager to see a full and proper review by a fresh set of people.
It would be difficult to have a full and proper view on whether Rewa should be tried again without looking at all the evidence that now exists, Mr McKinnel said.
"There is new evidence that casts further light on various aspects of the Crown case and we are ready and willing to give it to the authorities for an objective review.
"It would be our preference to have a new set of people involved so they can cast a fresh and objective eye over all the evidence - old and new."
The last-surviving member of Ms Burdett's family, her brother Jim, said he was disappointed but not surprised that police would not investigate Rewa again.
He said that Solicitor-General Mike Heron phoned him some time ago to tell him that the stay against prosecuting Rewa again meant "nothing would happen".
Rewa was convicted of Ms Burdett's rape in 1998 but two juries couldn't agree whether he murdered her.
Mr Pora was convicted of her rape and murder in 1994 and in 2000. The Privy Council this year ruled that new evidence that Mr Pora suffers from fetal alcohol syndrome was an explanation for contradictory confessions he made and quashed his convictions and recommended that he not be tried again.
Prime Minister John Key has since said it is now uncontested that Mr Pora did not commit the crimes.
The Privy Council said in its ruling that "it is not open to doubt" that Rewa was present when Ms Burdett was murdered.
Mr Bush said he had requested a review of the legal implications of a stay against a further prosecution of Rewa for the Burdett murder of granted at the conclusion of his second trial in 1998.
A spokeswoman for Mr Heron said compelling evidence that was not available at the 1998 trials would be required for the stay to be lifted.
Jim Burdett said it was "better than nothing" that the police plan to discuss the stay with Crown Law.
"This thing isn't over."
He noted that Mr Pora, whom he met for the first time last month, had not yet been found to be innocent.
Former High Court judge Rodney Hansen, appointed this week to conduct the inquiry into Mr Pora's claim for compensation, would determine whether Mr Pora is innocent on "the balance of probabilities".
"I'd be surprised if they don't feel that on the balance of probabilities that he didn't do it," Mr Burdett said. "That is the basis I had been working on myself. The more I thought about it, the more it seemed that it was improbable he had done it."
Of his 45-minute meeting with Mr Pora, Mr Burdett said: "He seemed very genuine and a gentle character."