The subject of the invention is separation on a solid support by multi-column sequential selective retention in order to separate a product of interest from a solution containing such a product of interest, by passing this solution over a fixed chromatographic resin bed comprising at least three zones, liquid flow means being placed between adjacent zones and between the last zone and the first zone, this process comprising several sequences, each sequence comprising at least one step chosen from an absorption step, a rinsing step and a desorption step, carried out either simultaneously or not, each following sequence is carried out by the displacement of the fronts in the zones towards the downstream end substantially of the same increment before the periodic displacement of the points of introduction and of withdrawal, characterized in that the process includes a sub-sequence without injection of the charge.