The present invention is directed to a process for forming a well visible non-chromate conversion coating on surfaces of magnesium and magnesium alloys, to a composition therefor and to a method of use for such coated articles having surfaces of magnesium or any magnesium alloy. The composition is a solution or dispersion comprising a fluorosilicon acid. The composition is preferably an aqueous solution having a pH in the range from 0.5 to 5 and includes often at least one pH adjustment agent. The thereof formed coating is useful to increase the corrosion resistance and the adhesion of magnesium and magnesium alloys to a paint coating, powder coating, e-coat, fluoropolymer coating, self-lubricant layer and adhesive bonding layer. The conversion coating may favorably be coated with a fluoropolymer coating, coated with a silane based sealing or both. The such formed coating is typically of grey mat non-metallic appearance.