A muffler for an internal combustion engine or the like including a casing (21) having an inlet opening (28), an outlet opening (29), a first partition (43) secured in the casing (21) to divide incoming exhaust gases, and a second partition (46) secured in the casing (21) downstream of the first partition (43), which second partition (46) has an opening (39) through which the divided exhaust gases are converged and joined together for exiting the casing (21). The improvement in the muffler assembly which produces both sound attenuation and lower operating back pressure is to provide an intermediate partition (51) secured in the casing between the first and second partitions (43,46) which is formed to permit substantially uninterrupted or unimpeded flow of exhaust gases past the intermediate partition, while a forwardly facing concaved surface (52) reflects sound components in a direction away from the opening (39) in the second partition (46). A method of attenuating sound and reducing back pressure comprising the step of securing an intermediate partition (51) between the first and second partitions (43,46) is provided.