A postal sorting machine for flat articles on edge, said machine comprising first belt conveyor means suitable for conveying said flat articles along a first path, a plurality of sorting outlets, each of which is associated with a separator flap mounted to move about a pivot axis between a first position in which it does not interfere with said first path and a second position in which it intersects said first path so as to direct said flat articles along a second path, said separator flap being suspended by a pivot rod extending on one side of said flap only, so that the zone under said separator flap is left free.