Hitching assembly for a towing motor vehicle

The assembly has an attachment (6) including a ball coupling (7) and an cover attachment (8) that are fixed on an assembly plate, where the plate is secured to a coupling bar (4) using a fixing unit (5). The fixing unit comprises brackets, where each bracket presents a pair of wings. The wings of the one of the brackets are fixed on two opposite faces of the coupling bar while the wings of the other bracket define a plane on which the plate is fixed. A support (13) supports a bearing plate so as to imprison and to tighten the bar.