Method for coating the surface of a metal substrate, comprising the following steps: A. providing the metal substrate, B. coating the substrate surface in a plasma polymerisation reactor by means of plasma polymerisation, wherein - in step B, (a) precursor(s) consisting of one or more organosilicon compounds or (b) precursor(s) consisting of one or more organosilicon compounds and further compounds are used for the plasma, and - in step B, the metal substrate is arranged in the plasma polymerisation reactor in such a way that the metal substrate is connected as a cathode, characterised in that the method is conducted in such a way that the coating produced by the method has - a strain to microcracking of ≥ 1.5%, - a yellow index determined according to ASTM D 1925 of ≥ 4 and - a hardness to be measured by means of nanoindentation in the range of 2.5 to 10 GPa, - a carbon content, determinable by measurement using XPS, of 3 to 28 atom%, based on the total number of carbon, silicon and oxygen atoms contained in the coating, with the proviso that the metal substrate is not a light metal substrate and with the proviso that in the case of a strain to microcracking of the coating of ≥ 2.2%, the hardness to be measured by means of nanoindentation is ≥ 6 GPa, wherein - the ratio of the gas flows of oxygen and the precursor(s) supplied to the plasma in step B lies in the range of 1:1 to 6:1 and - during step B, a control is performed, so that the self-bias lies in the range of 50 to 1000 V. A. providing the metal substrate, B. coating the substrate surface in a plasma polymerisation reactor by means of plasma polymerisation, wherein - in step B, (a) precursor(s) consisting of one or more organosilicon compounds or (b) precursor(s) consisting of one or more organosilicon compounds and further compounds are used for the plasma, and - in step B, the metal substrate is arranged in the plasma polymerisation reactor in such a way that the metal substrate is connected as a cathode, characterised in that the method is conducted in such a way that the coating produced by the method has - a strain to microcracking of ≥ 1.5%, - a yellow index determined according to ASTM D 1925 of ≥ 4 and - a hardness to be measured by means of nanoindentation in the range of 2.5 to 10 GPa, - a carbon content, determinable by measurement using XPS, of 3 to 28 atom%, based on the total number of carbon, silicon and oxygen atoms contained in the coating, with the proviso that the metal substrate is not a light metal substrate and with the proviso that in the case of a strain to microcracking of the coating of ≥ 2.2%, the hardness to be measured by means of nanoindentation is ≥ 6 GPa, wherein - the ratio of the gas flows of oxygen and the precursor(s) supplied to the plasma in step B lies in the range of 1:1 to 6:1 and - during step B, a control is performed, so that the self-bias lies in the range of 50 to 1000 V. - in step B, (a) precursor(s) consisting of one or more organosilicon compounds or (b) precursor(s) consisting of one or more organosilicon compounds and further compounds are used for the plasma, and - in step B, the metal substrate is arranged in the plasma polymerisation reactor in such a way that the metal substrate is connected as a cathode, characterised in that the method is conducted in such a way that the coating produced by the method has - a strain to microcracking of ≥ 1.5%, - a yellow index determined according to ASTM D 1925 of ≥ 4 and - a hardness to be measured by means of nanoindentation in the range of 2.5 to 10 GPa, - a carbon content, determinable by measurement using XPS, of 3 to 28 atom%, based on the total number of carbon, silicon and oxygen atoms contained in the coating, with the proviso that the metal substrate is not a light metal substrate and with the proviso that in the case of a strain to microcracking of the coating of ≥ 2.2%, the hardness to be measured by means of nanoindentation is ≥ 6 GPa, wherein - the ratio of the gas flows of oxygen and the precursor(s) supplied to the plasma in step B lies in the range of 1:1 to 6:1 and - during step B, a control is performed, so that the self-bias lies in the range of 50 to 1000 V.