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The court announced its decision on Wednesday in Canberra.
Pell, 78, was found guilty by a jury of the rape of a 13-year-old choirboy and sexual assault of another at St Patrick's Cathedral in Melbourne in 1996, but he has always denied any wrongdoing.
The Victorian Court of Appeal in August upheld a jury verdict convicting Pell in a 2-1 ruling.
Pell is serving a six-year jail term and is ineligible for parole until he has served three years and eight months of his sentence.