A metal sheet, inclusive of a metal strip, having a front side and a back side, both the front side and the back side comprising a first coating having an average thickness in the range from 0.5 to 10 μm, wherein the first coating of the front side contains particles, which release divalent or multivalent metal ions upon the action of an acid, in such an amount that a self-depositing coating agent forms, upon contact with the front side, a second coating thereon, whereas this is not the case for the first coating of the back side. The first coating of the front side can be overcoated with a self-depositing coating agent. Cut edges that do not have a first coating can be covered with the self-depositing coating agent. Correspondingly coated metal sheets, as well as a method for the manufacture thereof, are furthermore within the scope of the invention.