In a regenerative reforming facility using a series of moving beds, a direct supply of regenerated catalyst, optionally reduced is passed into at least two of the reactors of the series. Spent catalysts from different reactors are passed into a common mixing apparatus so as to provide a homogeneous degree of coke on the spent catalysts which are thereafter passed to a regenerator. The feedstock and the intermediate effluents continue to circulate in succession relative to the reactors. The invention makes it possible in particular to reduce the operating pressure of the units to less than 0.2 MPa.