Proposed is a method for providing uniform distribution of plasma density in a CCP plasma processing apparatus. According to the method the through gas holes of the showerhead of used in the plasma processing chamber of the apparatus are provided with conical nozzles formed on the side of the gas holes that face the gas reservoir of the cooler plate. The cone angle θ of the nozzles decreases in the direction from the peripheral portion to the central area of the showerhead in the range from 120° to 0°. Since the conical nozzles increase the gas gap between the showerhead and the cooler plate, more favorable conditions are created for electric breakdown. In order to protect the surfaces of the conical nozzles and gas holes from deterioration by hollow cathode discharge, these surface are coated by a protective coating resistant to electrical breakdown and chemical corrosion.