A system in which the depollution means (1) are associated with oxidation catalyst-forming means (2), and the engine (4) is associated with common manifold means (7) for feeding it with fuel, and adapted to implement a regeneration strategy in at least one operation of post-injecting fuel into the cylinders, is characterized in that is comprises: detector means (8) for detecting a regeneration request (req.RG); detector means (9) for detecting a state of the foot being raised on the vehicle accelerator; temperature acquisition means (11) for acquiring the temperature downstream from the catalyst-forming means (2); means (8) for determining a maximum quantity of fuel to be injected in the post-injection operations during the period of returning to idling following the foot being raised, and on the basis of said temperature; and means (7, 8) for immediately interrupting the post-injection operation as soon as the quantity of fuel injecting has reached the maximum quantity.