How to Taper Off Prednisone Dosage. When the vet establishes that the dog no longer needs prednisone treatment, the dose cannot be simply discontinued starting from the following day, because the dog can get severely ill. The prednisone should be gradually tapered off. The vet may decide to taper off prednisone by halving the daily dose or administering a normal dose every second day to the dog. After one week, the dog can get less prednisone, or get the initial dose of prednisone once every three days.