A wafer W is processed by supplying a two-fluid, high pressure jet water, or mega-sonic water onto the wafer W, while rotating the wafer W in an essentially horizontal state. After supply of the cleaning fluid is stopped, the wafer W is dried by rotating the wafer W at a higher speed than that used in supplying the cleaning fluid. No rinsing process using purified water is performed in a period after stopping supply of the cleaning fluid and before rotating the substrate at the higher speed.