Internal combustion engine

In a self-igniting possible range, both intake and exhaust valves (6), (7) are placed in a closure condition for a period from the end of an exhaust stroke and the beginning of an intake stroke for establishing a negative overlap period in which a residual gas is pressurized to increase its temperature, thus raising the air fuel mixture temperature in a combustion chamber (3) up to a compression ignition possible temperature. And, a fuel is for the first time injected from an in-cylinder injector (11) during an intake stroke in a high-load operating condition, and the fuel is for the second time injected in the second half of a compression stroke. Thus, the fuel is twice injected so that preignition may be prevented.