A particulate filter arranged in an engine exhaust passage is provided with alternately arranged exhaust gas inflow and outflow passages and porous partition walls which separate these passages from each other. In each partition wall, a coated zone where a coated layer with an average pore size smaller than that of a partition wall substrate is used to cover the substrate surface and a non-coated zone downstream of the coated zone where the substrate surface is not covered by said coated layer, are defined, and the ash in the exhaust gas can pass through the partition wall in the non-coated zone. Judgment processing which judges if a particulate matter trapping rate of the particulate filter has fallen below an allowable lower limit value is performed. PM removal processing is performed when it is judged that the particulate matter trapping rate has fallen below the allowable lower limit value.