Highly acidic catalysts stronger than the SO4/ZrO2 superacid with an acid strength of Ho less than or equal to-16.04 were obtained by kneading Zr(OH)(4) with ammonium sulfate together with chlorides of Ir, Pt, Rh, Ru, Os, and Pd followed by calcining in air at 600 degrees C, the metal concentration being equivalent to Pt of 7.5 wt% based on the hydroxide. The catalysts with Ir and Pt materials were highest in activity for the skeletal isomerization of butane to isobutane. The present catalysts were not obtained by treating the crystallized oxide, ZrO2 calcined at 700 degrees C, but the amorphous form followed by calcination to the crystallization.