An ignition system for an internal combustion engine includes an ignition transformer with two primary windings. The ignition system is designed to generate, for a given ignition event, a unipolar current through the secondary winding by way of a control circuit that is configured to first energize and deenergize the first primary winding to establish a first electrical arc across the spark-plug electrodes and, when the current in the secondary winding reaches, or drops below, a current threshold, repeatedly energizes and deenergizes the second primary winding to establish a plurality of second current pulses across the electrodes in order to maintain the burn phase.