A method for controlling a supercharged engine, that includes determining an overlap of valves by opening a supercharged non-fuel-containing air inlet valve and closing an exhaust valve before the exhaust phase of an engine cylinder and in the vicinity of the top dead center (TDC), actuating a blocking means for blocking a supercharged non-fuel-containing air intake means to admit supercharged air flowing in the supercharged non-fuel-containing air intake means into a chamber to scavenge residual burned gases when a pressure of the supercharged non-fuel-containing air is greater than a pressure of the exhaust gases, and actuating the blocking means to shut off the supercharged air flowing from the supercharged non-fuel-containing intake means into the chamber when pressure of the supercharged non-fuel-containing air is less than pressure of the exhaust gases.