The invention relates to a muffler (S) intended to be mounted in an exhaust line (L) of a heat engine (M), said muffler comprising one or more shells defining three volumes (1a, 1b, 2), referred to as upstream (1a), intermediate (1b) and downstream (2), arranged in succession and passed through by a plurality of pipes including: a supply pipe (10) for feeding the exhaust gases from the engine (M) into the intermediate volume (1b) via the upstream volume (1a); a so-called forward path pipe (12) for bringing the exhaust gases from the intermediate volume (1b) into the downstream volume (2); a so-called return path pipe (13) for feeding the exhaust gases from the downstream volume (2) into the upstream volume (1a) via the intermediate volume (1b); and a discharge pipe (14, 14') provided predominantly outside the shell(s) and leading out of the upstream volume (1a).