A process for preparing an amine by reacting an aldehyde and/or ketone with hydrogen and a nitrogen compound selected from the group of primary and secondary amines in the presence of a heterogeneous catalyst, wherein the catalyst is a coated catalyst which comprises at least one metal of group VIII of the Periodic Table of the Elements as a hydrogenating metal and additionally a promoter on an oxidic support, at least 80% of the metal of group VIII of the Periodic Table of the Elements being present in a layer between the surface of the catalyst and a penetration depth which is not more than 80% of the radius of the catalyst, calculated from the surface of the catalyst.