A supercharged internal-combustion engine has at least two cylinders with a combustion cycle during which a cylinder (10) of the engine is in the intake phase with burnt gas scavenging in the vicinity of the top dead center (TDC) thereof while another cylinder is in the exhaust phase in the vicinity of the bottom dead center (BDC) thereof, the cylinders having at least one intake (12) with an intake valve (14.sub.1, 14.sub.2, 14.sub.3, 14.sub.4) and at least one exhaust (18) with an exhaust valve (20.sub.1, 20.sub.2, 20.sub.3, 20.sub.4). Controlling the engine includes carrying out scavenging of the burnt gases of the cylinder in the intake phase by a valve overlap stage by opening simultaneously its exhaust (20.sub.1) and intake (14.sub.1) valves, and controlling opening of exhaust valve (20.sub.3) of the cylinder in the exhaust phase so that, during at least part of the overlap stage, the exhaust pressure (Pe) of the cylinder in the intake phase is lower than its intake pressure (Pa).