A polybenzoxazine sulfide has repeating units including at least one unit corresponding to formula (I) or (II): in which the two oxazine rings are connected together via a central aromatic group, the benzene ring of which bears one, two, three or four groups of formula —Sx—R in which “x” is an integer from 1 to 8 and R represents hydrogen or a hydrocarbon-based group including 1 to 10 carbon atoms and optionally a heteroatom chosen from O, S, N and P. Such a polybenzoxazine can be used as an adhesive layer on metal, in particular for the adhesive bonding of a metallic substrate, in particular made of carbon steel, to rubber.