The planar conveyor belt is designed to move along curved trajectories and has a plurality of chain-links including, staggered at the fronts and at the rear of a central core, a succession of slots, each with an opening, in particular oblong in shape, so as to ensure play in a longitudinal direction of a chain-link relative to another adjacent chain-link. The conveyor belt is characterized in that at least on the side external to the curved trajectory it is designed to follow, at least some of the chain-links include, in their transverse extension, a chain-link modules providing, in particular across its slots a curvilinear contact zone with the pivot pins linking them.