David Gilroy was sentenced to life imprisonment and ordered to serve at least 18 years behind bars after being found guilty of murdering his ex-lover Suzanne Pilley and attempting to defeat the ends of justice.
The Supreme Court in London has now refused his application to have his case reviewed.
Gilroy went on trial at the High Court in Edinburgh in February 2012 and was convicted of murder in March that year following a 17-day trial. Ms Pilley's body has never been found.
The jury heard he was driven by jealousy, maintained a front of normality and embarked on a series of acts to cover up his crime.
He was convicted by a majority verdict after the prosecution argued that Gilroy killed Ms Pilley because she tried to break off their two-year relationship. He took 38-year-old Ms Pilley's body to a secret grave, believed to be in remote Argyll near the Rest and Be Thankful pub.
Married Gilroy has protested his innocence since the day Ms Pilley vanished from the Edinburgh city centre business premises where she worked alongside him.
Judge Lord Bracadale told Gilroy, 49, when he was convicted that he hoped he would one day say where he abandoned the victim's body.
Gilroy's case made legal history when he became the first convicted killer to have his sentencing filmed for British TV though the camera focused only on the judge, Lord Bracadale.