The sulfidation resistance of a silver-base material coating is further improved by making a concentration gradient of silver, oxygen and of one or more oxidizable alloying elements that may be present in the material, from the free surface of the coating up to a depth comprised between 10 nm and 1 μm and more particularly between 100 nm and 1 μm. Thus, the coating comprises a stack of one main layer made from silver-base material and of one oxidized thin film. The thin film, with a thickness comprised between 10 nm and 1 μm, thus presents a decreasing silver concentration gradient from the interface between the thin film and the main layer to the free surface of the thin film. Deposition of the coating on a support can be achieved by two successive physical vapor deposition steps, and more particularly by magnetron cathode sputtering.