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Jules Mikus, 52, was sentenced to preventive detention in 2002 for raping and murdering the six-year-old in 1987.
In May Mikus appeared in the Court of Appeal and argued he needed more time to prove his innocence.
A number of lawyers had refused to take on the case which was why his application for appeal had taken so long, he told the court.
Mikus also argued that two DNA samples taken from him in 1987 and 2002 did not match.
He asked for counsel to be appointed to assist him and for further DNA testing.
Crown prosecutor Lisa Preston told the court the two DNA samples were identical and Mikus had misinterpreted the tests results.
In a judgment released today Justice Susan Glazebrook, on behalf of a three-judge bench, declined his application for an extension of time to appeal.
"None of the proposed appeal grounds have any merit," the judgment said.
The application for the appointment of counsel and for orders for further DNA testing was also declined.