The invention relates to 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 conversion layer comprising:



zincsulphate hydrate,
aluminium in an amount up to 14 mg·m−2,
wherein the conversion layer comprises neither zinc hydroxysulphate, nor free water molecules nor any compounds having free hydroxyl groups, the surface density of sulphur in the conversion layer being greater than or equal to 5.0 mg/m2. The invention also relates to the corresponding treatment method.