A welding unit for welding two rails of a track is equipped with clamping jaws intended for lying against a rail web. The clamping jaws each have a sliding surface, which is at a distance from a contact surface in the transverse direction of the rail and is arcuately curved with respect to a cross section extending such that it is normal to a neutral axis of the rails. The jaw mount, intended for fixing the clamping jaw, has a sliding surface, which is curved in a way corresponding to the sliding surface of the clamping jaw, and so the clamping jaw is movable along the sliding surfaces in relation to the jaw mount.