Preparing a primary amine by alcohol amination of alcohol with ammonia and elimination of water includes reacting, in a homogeneously catalyzed reaction, a mixture of alcohol, ammonia, nonpolar solvent, and catalyst, in a liquid phase, to obtain a product mixture. The process then includes phase separating the product mixture into a polar product phase and a nonpolar product phase, and separating off the nonpolar product phase. At least some of the nonpolar phase returns to the homogenously catalyzed reaction. The process further includes separating off amination product from the polar product phase. At least some of the catalyst is in the nonpolar phase, and the catalyst accumulates in the nonpolar phase.