A Method for the immobilization of biomaterial on a substrate with an Si.sub.3 N.sub.4 surface to which the biomaterial is covalently bonded by means of a hetero-bifunctional cross-linking agent, said method comprising the steps of providing a substrate with a Si.sub.3 N.sub.4 surface having Si--NH.sub.2 groups to provide reactive NH.sub.2 groups, providing a hetero-bifunctional cross-linking agent having an NH.sub.2 -reactive group selected from the group consisting of aldehyde, ester, halogenide, epoxide, imine and isocyanate, and a biomaterial-reactive group, reacting a biomaterial with the biomaterial-reactive group of the cross-linking agent to covalently bond the biomaterial to the cross-linking agent, and reacting the NH.sub.2 -reactive group of the cross-linking agent with the NH.sub.2 groups of the Si.sub.3 N.sub.4 surface to covalently bond the cross-linking agent to the surface and mobilize the biomaterial on the Si.sub.3 N.sub.4 surface of the substrate.