To provide an improved rapier tape head having a crest provided with anchorage holes fixed orthogonally to the rapier tape.

The fixing of the crests is realized by using connection elements (5) of a thermoplastic resin and a material entering into holes (6a, 6b) which encloses a part of the crest and extends along the rapier tape head. The end of the assembly formed by the rapier tape and the crest is shaped such to pack-tighten the surface of the gripper (1) between the surface of the rapier tape (3) and the surface of an overlying bracket extension (7, 8, 9)of the stiffening crest (4). There can be continuous or localized (interrupted) projecting blocks in the part below the rapier tape (3), with support functions of the rapier tape head (2), to couple with the solution of the gripper projecting from the lower surface of the rapier tape (3), to ensure the optimal positioning of the rapier tape head (2) with respect to the traverse path, along the pathway in the shed.