An exhaust line includes a duct having an injection segment with an inner channel defined by a side wall. The exhaust gas flow includes exhaust gas central streams in a central area of the inner channel and exhaust gas peripheral streams in the vicinity of the side wall. A reagent injector injects a reagent in an injection direction. The duct (3) is conformed so that the exhaust gas central streams flow substantially parallel to the central line of the inner channel. The exhaust line includes an element that imparts, to at least some peripheral streams, a rotary movement through the inner channel; and about a rotation axis that is slightly inclined relative to the injection direction.