The invention relates to a clamp constituted by a band of metal comprising, at each one of its ends, complementary tightening and/or fastening means, whereas the inner end of the band comprises an extension which goes beyond the corresponding fastening means, under the outer end of the band.In this clamp, the transversal edge of the band, which constitutes the free end of the extension, has a profile indented into the band, such as an .OMEGA.-shaped profile, whereas close to its outer end, and on this side of the corresponding tightening and/or fastening means, said band comprises an elongated boss, which projects from its inner face, and is adapted to penetrate into the indented profile of the free end of the extension, said boss having its maximum height substantially equal to the thickness of the band.