An ignition device has a high voltage transformer having a primary side and a secondary side, of which the primary side is connected to a high voltage source and the secondary side is connected to a spark path to provide the ignition spark. The time variation in the primary current flowing on the primary side is measured and subdivided at least into a spark burning phase and a subsequent free-running phase of the high voltage transformer. The transition from the spark burning phase into the free-running phase is equated to the moment of extinction of the ignition spark. The time variation of the primary current in the spark burning phase is mapped by a first function and in the free-running phase by a second function, and the intersection point of the two functions is equated to the moment of extinction of the ignition spark.