For co-production of metaxylene and paraxylene from a hydrocarbon feedstock in a simulated moving bed in a chromatographic column (1) that contains a number of beds 1, 2,3, 4 . . . of an adsorbent, interconnected in a loop, the column comprises an injection of the feedstock, a draw-off (14) of a first raffinate, a draw-off (17) of a second raffinate that comprises metaxylene, an injection of desorbent and a draw-off of an extract that delivers paraxylene. The injection positions and the draw-off position of the extract are offset periodically by one bed in the direction of flow of the main flux that circulates in the column. First raffinate (14) that comprises desorbent, orthoxylene, metaxylene and ethylbenzene is drawn off continuously or intermittently, and second raffinate (17) R2 that comprises orthoxylene and metaxylene is drawn off intermittently. The second raffinate is distilled in such a way as to recover orthoxylene and metaxylene separately with at least 99% purity and with an improved yield. The resultant xylenes are suitable for the production of isophthalic acid and terephthalic acid