The man convicted of the rape and murder of Auckland woman Blessie Gotingco has exhausted all avenues of appeal.

The Supreme Court has rejected Tony Robertson's leave to appeal his conviction, ruling there was no miscarriage of justice.

Robertson claimed his case raised questions about the general importance of when directions might be given in a murder case.

His lawyers had also argued that a "substantial miscarriage of justice may occur because there was no direction as to the availability of a manslaughter verdict.

Robertson's earlier bid to the Court of Appeal complaining his conviction was unsound and his sentence unfair was also turned down in April.

At Robertson's High Court trial, he denied intending to kill Gotingco, saying the injuries she sustained when struck by his car were accidental. He claimed to be acting without murderous intent at the time he stabbed her because she was already dead.

Robertson also denied the rape, saying evidence had been planted by police.

When it got to the Court of Appeal, Robertson kept the same objections, and also claimed he was so wasted on drugs it was impossible to have an intent to murder and that Gotingco was possibly dead before being stabbed.

Robertson asserted that no rape could have happened because Gotingco had already died and a rape victim had to be living.

However, the Court of Appeal judges did not accept these claims and rejected his bid for appeal.

Robertson had previously appealed his 2006 conviction for the abduction and indecent assault on a child to the Supreme Court.

He has never admitted responsibility for any of the serious crimes for which he has been convicted.