The soundproofed exhaust duct for a turbine engine comprises a perforated inner shell defining a flow passage, and a solid outer shell, the inner and outer shells defining between them a space that is closed at the upstream and downstream ends of said space. A core extends between the inner and outer shells at a distance therefrom, and contains at least one sound energy dissipating layer made up of hollow beads that are held against one another. A frame with upstream and downstream portions connected together by longitudinal members supports the core and partitions it into a plurality of boxes that are filled with hollow beads that are held between perforated textures, the frame being secured to the outer shell and/or to the inner shell via at least one of its upstream and downstream portions.