Coextrusion head for a complex rubber profile intended for the manufacture of a tire, the head destined to be mounted on a coextrusion machine with a cylindrical roller and comprising, for this purpose, a lower wall with a cylindrical profile extending radially lengthwise in a longitudinal direction about a central axis and extending rectilinearly widthwise in a transverse direction parallel to the central axis and perpendicular to the longitudinal direction, the head comprising, from upstream to downstream of this lower wall with a cylindrical profile and in the longitudinal direction: a) a first extrusion channel opening into the lower wall of the coextrusion head, this first extrusion channel being separated into different sub-channels (60-1,60-2,60-3,60-4) in the transverse direction, b) a first profiling blade defining a first profiling profile that is discontinuous in the transverse direction and lies radially beyond the lower wall of the coextrusion head intermittently in the transverse direction, c) a second extrusion channel opening into the lower wall of the coextrusion head, this second extrusion channel being separated into different sub-channels (64-1, 64-2, 64-3, 64-4) in the transverse direction, d) a second profiling blade defining a second profiling profile discontinuous in the transverse direction and located radially beyond the lower wall of the coextrusion head intermittently in the transverse direction, this second profiling blade incorporating at least one third extrusion channel (68-1, 68-2, 68-3) opening into the lower wall of the coextrusion head, the coextrusion head being characterized by at least one outlet (70-1, 70-2, 70-3) of this third channel being located in the extension in the longitudinal direction of a separating element (72-1, 72-2, 72-3) separating the first extrusion channel into sub-channels (60-1, 60-2, 60-3, 60-4) in the transverse direction, creating a discontinuity in the first profiling profile of the first profiling blade in the transverse direction, and separating the second extrusion channel into sub-channels (64-1, 64-2, 64-3, 64-4) in the transverse direction, and in that e) a third profiling blade defines a final profiling profile located radially beyond the bottom wall of the coextrusion head, this final profiling profile having no discontinuity in the transverse direction, but comprising a tooth (74-1, 74-2,74-3) projecting in front of and next to each outlet (70-1,70-2,70-3) of a third channel (68-1,68-2,68-3) in the transverse direction, each tooth (74-1,74-2,74-3) extending radially inwardly but not reaching the bottom wall of the coextrusion head. a) a first extrusion channel opening into the lower wall of the coextrusion head, this first extrusion channel being separated into different sub-channels (60-1,60-2,60-3,60-4) in the transverse direction, b) a first profiling blade defining a first profiling profile that is discontinuous in the transverse direction and lies radially beyond the lower wall of the coextrusion head intermittently in the transverse direction, c) a second extrusion channel opening into the lower wall of the coextrusion head, this second extrusion channel being separated into different sub-channels (64-1, 64-2, 64-3, 64-4) in the transverse direction, d) a second profiling blade defining a second profiling profile discontinuous in the transverse direction and located radially beyond the lower wall of the coextrusion head intermittently in the transverse direction, this second profiling blade incorporating at least one third extrusion channel (68-1, 68-2, 68-3) opening into the lower wall of the coextrusion head, the coextrusion head being characterized by at least one outlet (70-1, 70-2, 70-3) of this third channel being located in the extension in the longitudinal direction of a separating element (72-1, 72-2, 72-3) separating the first extrusion channel into sub-channels (60-1, 60-2, 60-3, 60-4) in the transverse direction, creating a discontinuity in the first profiling profile of the first profiling blade in the transverse direction, and separating the second extrusion channel into sub-channels (64-1, 64-2, 64-3, 64-4) in the transverse direction, and in that e) a third profiling blade defines a final profiling profile located radially beyond the bottom wall of the coextrusion head, this final profiling profile having no discontinuity in the transverse direction, but comprising a tooth (74-1, 74-2,74-3) projecting in front of and next to each outlet (70-1,70-2,70-3) of a third channel (68-1,68-2,68-3) in the transverse direction, each tooth (74-1,74-2,74-3) extending radially inwardly but not reaching the bottom wall of the coextrusion head.