A method for making a biocompatible medical article, and preferably, a blood compatible medical article, through the use of a copolymer coating. The copolymer coating is synthesized using methacrylate or acrylate monomers with a functional group (primary amino group) for subsequent attachment of a biomolecule such as heparin. Synthesis of the copolymer coating is carried out using the proper proportion of hydrophobic monomer/hydrophilic monomer/functional monomer in order to optimize the solubility of the copolymer in alcohol, its insolubility in water (before and after heparin coupling), the heparin coupling efficacy and heparin bioactivity. Once the copolymer coating is fashioned, a medical article is coated with it. The coating is thereafter dried and the biomolecule, such as heparin, attached. In such a manner the present invention provides for a method for making a biocompatible medical article, and preferably, a blood compatible medical article.