The invention concerns polyurethane (PUR) having an antithrombogenic coating, wherein the antithrombogenic coating comprises at least one antithrombogenic substance covalently bound to a surface of the PUR via at least two bonds, wherein a first of said bonds is an amide bond between the surface of the PUR and a polyethyleneimine (PEI) and a second of said bonds is between the PEI and the antithrombogenic substance, wherein the surface of the PUR had been activated by use of a carbon dioxide plasma or a plasma modified by addition of carbon dioxide before the first of said bonds was formed.