This invention relates to a band clamp fitting constituted by a metal band wound on itself, presenting, near one of its ends, an ear provided with an extension and, at the other end, a hook. The extension presents a projecting part, of transverse dimension less than that of the free edge of the hook and capable of cooperating with pre-hooking means when the clamp fitting is in non-tightened state. The free edge of the hook presents a notch, of dimensions adapted to those of the projecting part and offset with respect to the latter in the transverse sense of the band. A portion of the free edge of the hook is located in line with the projecting part and is capable of being hooked therebehind.