warp yarn 16 is re woven so as to be superposed onto itself because it is folded back at the end of the strip in a manner that is orthogonal to the plane of the strip during manufacture of the woven strip of the invention weft yarns having a diameter d are replaced in each re weaving zone at the end of the strip by means of weft yarns having a smaller diameter d so that after the warp yarns have been re woven over the front and back faces of the strip the thickness h u2032 of the strip in the re weaving zones b is the same as the thickness h of the main body a of the strip for a woven strip having a single plane of weft yarns the difference between the diameter of the weft yarns in the main body a of the strip and the diameter of the weft yarns in the re weaving zones b is equal to twice the thickness of a flat section warp yarn such as 16 during the operation of re weaving the warp yarns the ends of these warp yarns are brought out through the back face 26 of the strip at different locations along the strip depending on the weave pattern defined by the warp yarn in question so.