The postal sorting machine has sorting outlets in which mailpieces are accumulated, said sorting outlets being disposed in line along a certain longitudinal axis. It further includes a recirculation device for recirculating the mailpieces stored in the sorting outlets, this device comprising a belt (40) mounted to move along the sorting outlets and to which cleats (41, 42) are fastened to define a succession of compartments (4a, 4b, 4c) that face respective ones of the sorting outlets, each compartment being arranged to store, on edge, mailpieces taken from a corresponding sorting outlet.