A system in which a depollution apparatus 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. A request (req.RG) for regeneration is detected, state in which the vehicle accelerator pedal is being raised or a stage in which the engine is idling is detected, the temperature downstream from the catalyst is acquired, and a maximum quantity of fuel to be injected during post-injections is determined. The post-injection is immediately interrupted if the quantity of fuel injected reaches the maximum quantity during a stage of returning to idling. The post-injection is progressively reduced if the quantity of fuel injected reaches the maximum quantity during a stage of idling.