A process for anticorrosion treatment of bare metal surfaces comprising steel surfaces, comprising contacting the bare metal surfaces with an acidic aqueous solution of a fluoro complex of at least one element M selected from the group B, Si, Ti, Zr and Hf, at least one further component selected from among: a buffer system for the pH range from 2.5 to 5.5, nitrate ions, copper ions, silver ions, vanadium or vanadate ions, bismuth ions, magnesium ions, zinc ions, manganese ions, cobalt ions, nickel ions, tin ions, aromatic carboxylic acids with at least two groups containing donor atoms, or derivatives of such carboxylic acids, and silica particles with an average particle size of below 1 μm; and contains no more than 1 mg/l of an organic polymer with allylamine or vinylamine monomers; then rinsing the metal surfaces with water and thereafter coating them with a cathodically depositable electro-dipcoating.