The subject matter of the present invention is a multi-step method for the anti-corrosive coating of metal components, in which a reaction rinse is used after a conversion treatment but before electrodeposition is carried out on the component. The conversion treatment includes first the deposition of a thin inorganic layer containing the elements Zr and/or Ti. The metal component is then treated with a reaction rinse containing a surface-active substance and is subsequently subjected to electrodeposition.