The invention relates to a method of flushing an extracorporeal blood circuit, preferably an extracorporeal blood circuit of a dialysis machine, with a flushing liquid, wherein the flushing liquid contains an anticoagulant agent, preferably heparin. The invention further relates to an extracorporeal blood treatment unit, preferably to a dialysis machine, having an extracorporeal blood circuit and a control unit, wherein the control unit is configured to carry out a flushing method in accordance with one of the preceding claims before the start of the treatment and/or intermittently during the treatment.