Patricia Hall vanished without trace from the family home in Pudsey, Leeds, West Yorkshire, in January 1992. A secretly taped alleged 'admission' by her husband, Keith, 39, that he strangled and dumped her body in an incinerator, was ruled inadmissible at Leeds Crown Court at his trial in March.
After studying police evidence at the end of the trial the Leeds coroner, David Hinchliff, applied to Mr Howard to hold an inquest even though Mrs Hall's body has never been found.
Mr Hinchliff said yesterday that he had been notified that after a lot of consideration, Mr Howard was not persuaded that an inquest would serve any useful purpose.
During Mr Hall's trial the prosecution claimed that he killed his wife because she wanted to divorce him and he feared losing his home, business and their two sons.
Mrs Hall's sister, Christine Weatherhead, said she was disappointed at the decision. 'It was a last chance to finally get some answers because the trial was a farce,' she said.