The invention consists in implanting an inner tube fed at its lower portion by a fraction of regenerated catalyst inside a riser (1) of an FCC unit that is fed by catalyst via a line (14) and a feedstock via a line (3), whereby the fluid that allows this feed can be inert, in which case a staging effect of the catalyst inside the riser or else a feedstock (14) that has a tendency toward a more severe cracking inside the inner tube, then leading to an additional production of olefins, in particular propylene, is advantageous. The mixtures of fluids and catalyst are cooled above the tube via a line (13) of an inert fluid.