The assembly for purification of exhaust gases comprises an upstream conduit and a downstream conduit positioned parallel to each other. A space has an exhaust gas inlet communicating with the upstream conduit and an exhaust gas outlet communicating with the downstream conduit. A middle line divides the inlet into first and second areas providing a same passage section to the exhaust gases.The assembly comprises a baffle covering at least 75% of the first area and covering less than 25% of the second area. The baffle and the space are laid out so that a portion of the exhaust gases penetrate through the first area of the inlet flows into the space along flow lines forming a cusp around the baffle.