A device for treating blood by extracorporeal circulation comprising a filter having a first chamber and a second chamber separated by a semi-permeable membrane. The device has an arterial line connected to the first chamber of the filter, a venous line issuing from the first chamber of the filter, a channel used for pre-infusion of a substance for regional anticoagulation and linked to the arterial line, a purge channel issuing from the second chamber of the filter, and an air separator on the venous line. The device also includes a line for post-infusion of a solution at least partially re-establishing the ionic equilibrium of the blood downstream of the air separator, the post-infusion line being configured immediately upstream of an air detector.