A method of coating the surface of a metal substrate includes a) applying a first composition on the surface of a metal substrate, the first composition being a solution comprising a liquid medium including sol-gel precursors of alcoxysilane type or of metallo-organic type; b) subjecting the first composition to first heat treatment to form an anchor layer on the metal substrate in which the sol-gel precursors are bonded to the metal substrate, a first temperature being imposed during the first heat treatment that is sufficient to eliminate all or part of the liquid medium and to encourage the bonding of the sol-gel precursors to the metal substrate; and c) applying a second composition on the anchor layer. The second composition includes coating compounds to obtain a coating on the anchor layer by forming bonds between the sol-gel precursors and the coating compounds.