A dialysis machine includes a dialyzer (1), a dialysate feed system (5) having a feed line (52), and a discharge system (6) having a discharge line (62). The machine further includes ultrafiltration control elements (UF) and back-filtration control elements (RF). The feed line is provided with a constriction (520) and with elements for measuring the pressure difference (523, 524) across the terminals of the constriction. The feed system further includes a ventricle bag (50), and pressurizer elements (70) for putting the ventricle bag (50) under pressure. The machine further includes an open/close system (C5, C5′) for opening/closing the discharge line (62) and the back-filtration control elements cause the discharge line (62) to close, and control the pressure applied to the ventricle bag (50), as a function of the pressure difference measured across the terminals of the constriction (520), so as to obtain a given flow rate of dialysate.