System in which the depollution device is associated with an oxidation catalyst, and the engine is associated with a common rail for feeding it with fuel and adapted to implement a regeneration strategy using at least one post-injection of fuel into the cylinders. In the system, a request for regeneration (req.RG) can be detected, whether the engine is in a stage of idling can be detected, a temperature downstream from the catalyst can be acquired, a maximum duration for post-injection application during the stage of idling can be determined on the basis of said temperature, and the post-injection can be progressively reduced as soon as the duration of use has reached the maximum duration.