Abstract: The invention relates to a dialysis machine comprising an arterial line (L1), a venous line (L2), a dialyser (100), a line for discharging (62) the dialysate, and a control unit (10) configured to perform a phase for rinsing the extracorporeal circuit by circulating physiological saline in the blood compartment of the dialyser and the arterial and venous lines, and a phase for eliminating air in the dialyser, which phase comprises stopping the circulation in the venous line (L2) and in the discharge line (62); and circulating dialysate from a dialysate supply source (40) through the blood compartment (12) and the arterial line (L1). The invention also relates to a method and a corresponding computer program product.