A head for the co-extrusion of a complex rubber profiled element intended for the manufacture of a tyre, the head being intended to be mounted on a cylindrical-roller co-extrusion machine and for this purpose comprising a lower wall of 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 of cylindrical profile, and in the longitudinal direction: a) a first extrusion unit comprising a first extrusion duct opening into the lower wall of the co-extrusion head, this first extrusion duct being divided into various sub-ducts (60-1, 60-2, 60-3, 60-4) in the transverse direction, b) a first profiling blade defining a first shaping profile that is discontinuous in the transverse direction and situated radially beyond the lower wall of the co-extrusion head intermittently in the transverse direction, c) a second extrusion unit comprising a second extrusion duct opening into the lower wall of the co-extrusion head, this second extrusion duct being divided into various sub-ducts (64-1, 64-2, 64-3, 64-4) in the transverse direction, d) a second profiling blade defining a second shaping profile situated radially beyond the lower wall of the co-extrusion head, this second profile having no discontinuity in the transverse direction but the second profiling blade comprising at least one tooth (67-1, 67-2, 67-3) extending radially inwards but not reaching the lower wall of the co-extrusion head, each tooth (67-1, 67-2, 67-3) being situated in the continuation of the longitudinal direction of a divider (72-1, 72-2, 72-3) dividing the first extrusion duct into sub-ducts (60-1, 60-2, 60-3, 60-4) in the transverse direction, creating a discontinuity in the first shaping profile of the first profiling blade in the transverse direction, and dividing the second extrusion duct into sub-ducts (64-1, 64-2, 64-3, 64-4) in the transverse direction, and this second profiling blade incorporating at least one third extrusion duct (68-1, 68-2, 68-3) opening into the lower wall of the co-extrusion head, and each outlet (70-1, 70-2, 70-3, 70-4) of a third extrusion duct closely adjoining a tooth (67-1, 67-2, 67-3), of the second profiling blade, and e) a third profiling blade defining a final shaping profile situated radially beyond the lower wall of the co-extrusion head, this final shaping profile having no discontinuity in the transverse direction, the third profiling blade comprising at least one tooth (74-1, 74-2, 74-3) extending radially inwards but not reaching the lower wall of the co-extrusion head, each tooth (74-1, 74-2, 74-3) of this third profiling blade being situated in front of a tooth (67-1, 67-2, 67-3) of the second profiling blade. a) a first extrusion unit comprising a first extrusion duct opening into the lower wall of the co-extrusion head, this first extrusion duct being divided into various sub-ducts (60-1, 60-2, 60-3, 60-4) in the transverse direction, b) a first profiling blade defining a first shaping profile that is discontinuous in the transverse direction and situated radially beyond the lower wall of the co-extrusion head intermittently in the transverse direction, c) a second extrusion unit comprising a second extrusion duct opening into the lower wall of the co-extrusion head, this second extrusion duct being divided into various sub-ducts (64-1, 64-2, 64-3, 64-4) in the transverse direction, d) a second profiling blade defining a second shaping profile situated radially beyond the lower wall of the co-extrusion head, this second profile having no discontinuity in the transverse direction but the second profiling blade comprising at least one tooth (67-1, 67-2, 67-3) extending radially inwards but not reaching the lower wall of the co-extrusion head, each tooth (67-1, 67-2, 67-3) being situated in the continuation of the longitudinal direction of a divider (72-1, 72-2, 72-3) dividing the first extrusion duct into sub-ducts (60-1, 60-2, 60-3, 60-4) in the transverse direction, creating a discontinuity in the first shaping profile of the first profiling blade in the transverse direction, and dividing the second extrusion duct into sub-ducts (64-1, 64-2, 64-3, 64-4) in the transverse direction, and this second profiling blade incorporating at least one third extrusion duct (68-1, 68-2, 68-3) opening into the lower wall of the co-extrusion head, and each outlet (70-1, 70-2, 70-3, 70-4) of a third extrusion duct closely adjoining a tooth (67-1, 67-2, 67-3), of the second profiling blade, and e) a third profiling blade defining a final shaping profile situated radially beyond the lower wall of the co-extrusion head, this final shaping profile having no discontinuity in the transverse direction, the third profiling blade comprising at least one tooth (74-1, 74-2, 74-3) extending radially inwards but not reaching the lower wall of the co-extrusion head, each tooth (74-1, 74-2, 74-3) of this third profiling blade being situated in front of a tooth (67-1, 67-2, 67-3) of the second profiling blade.