Conveyor belts are made from modular links having offset forward and rearward projecting eye parts to intercalate eye parts from one belt link between eye parts with oval lateral apertures. Connecting rods inserted through aligned apertures hingedly connect adjacent links. Clips restrict lateral turning of the belt links. Clips have general U-shapes with two legs, a bridge portion end, and opposite free ends. Projecting members at the free ends have lengths parallel to the legs and smaller than the lengths of the apertures in the belt links in which the clip is to be installed, and have heights equivalent to or smaller than the heights of the aperture in the belt link in which the clip is to be installed. The lateral distance between the two legs of the U, is larger than the lateral extent of an eye part in the belt link in which the clip is installed.