A steel substrate coated on at least one of its faces with a metallic coating based on zinc or its alloys wherein the metallic coating is itself coated with a zincsulphate-based layer—includes at least one of the compounds selected from among zincsulphate monohydrate, zincsulphate tetrahydrate and zincsulphate heptahydrate, wherein the zincsulphate-based layer has neither zinc hydroxysulphate nor free water molecules nor free hydroxyl groups, the surface density of sulphur in the zincsulphate-based layer being greater than or equal to 0.5 mg/m2. A corresponding treatment method is provided.