In a process for producing fatty acid methyl ester (FAME) from fats or oils by transesterification with methanol in the presence of an alkaline catalyst in at least two reaction stages traversed in succession, each consisting of a stirred-tank reactor and a downstream separator, a phase containing FAME and a phase containing glycerol are generated, which are separated in the separator, wherein the phase containing FAME is recirculated into the stirred-tank reactor of the next succeeding reaction stage and the phase containing glycerol is recirculated into the stirred-tank reactor of the first reaction stage, and the crude FAME withdrawn from the separator of the last reaction stage is transferred into a separator and the FAME withdrawn is dried. To increase the yield of FAME, the aqueous phase containing glycerol, methanol, undissociated soaps and FAME, which is obtained upon withdrawal of the FAME, is thoroughly mixed with the phases withdrawn from the separators of the first to penultimate reaction stages, which contain glycerol and FAME, and the mixture is separated in a separator into a phase containing FAME and a phase containing glycerol.