A medical apparatus for the extracorporeal treatment of blood or plasma comprises a semi-permeable membrane consisting of at least one electronegative polymer, such that the surface of the semi-permeable membrane has negative electric charges. Before the sterilization of the apparatus, and before or after the formation of the membrane, at least one cationic and anti-protease agent is incorporated in at least one part of the membrane, this agent undergoing bulk adsorption or semi-bulk adsorption in the membrane and/or being bound by an ionic interaction with the electronegative sites of the membrane.