The invention is a new self-locking clamp with a head (T) and a terminal end (C) comprising a linear element (L) with substantially rectangular section having one extremity connected to said head (T) and one rack provided with teeth (N), and wherein the sides of said teeth (N) are free and not constrained to or integral with any lateral ribs or shoulders. In particular, in each cross section of said terminal end (C) the thickness of said linear element (L) useful for bending is less than the overall height (h) of said terminal end (C).