Device for adjusting the relative position between a first part, for example a ski binding heel-piece, equipped with a toothed strip (8) and a second part, for example a slide (2), equipped with two opposed sets of teeth (16, 17) collaborating with the sets of teeth (10, 11) of the strip. The sets of teeth of one of the parts are offset by a half-tooth and the teeth of the sets of teeth are truncated. The sets of teeth of the two parts come into mesh alternately on one side and the other, making it possible to have a pitch for adjustment equal to a half-tooth rather than a full tooth. The fineness of the adjustment is thus improved.