Abstract: The muffler comprises a main sound arresting chamber formed in the interior of an outer cylinder of the muffler and a bracket fixedly secured to the outer surface of the outer cylinder for mounting the muffler on a body of a motorcycle. The muffler is provided with an auxiliary sound arresting chamber formed in the interior of the bracket and communicating with the main sound arresting chamber through a connecting passage so as to increase the total volume of the sound arresting chamber, thereby permitting the output of the engine of the motorcycle to be enhanced while the sound arresting effect on the exhaust gas is improved. The main sound arresting chamber may be divided into an upstream side main sound arresting chamber portion and downstream side main sound arresting chamber portions by partition means and the auxiliary sound arresting chamber portion communicates with the upstream main sound arresting chamber portion. The connecting passage may be in the form of a plurality of small diameter holes.