NOVELTY - Cation exchange resin is used, and fatty acid in raw material having animal and vegetable fats, is esterified with lower-alkyl alcohol to obtain reaction mixture containing ester mixed oil. Ester interchange of fats and oils in ester mixed oil is performed with lower alkyl alcohol, in presence of alkali catalyst. Soap by-produced at transesterification is decomposed with acid, and fatty acid is obtained. Fatty acid is returned at front stage side of esterification. Fatty acid lower alkyl ester is vacuum distilled from oil phase obtained at transesterification.    USE - For manufacturing fatty-acid lower alkyl ester used for light oil alternate fuel of motor vehicle, vessel, agricultural implement, machinery, construction machine, electric power generating apparatus and heating apparatus.    ADVANTAGE - The highly purified fatty acid lower alkyl ester is stably and economically manufactured with high yield.    DETAILED DESCRIPTION - A cation exchange resin is used, and fatty acid in raw material containing animal and vegetable fats, is esterified with lower-alkyl alcohol. A reaction mixture containing ester mixed oil having acid value of 2 or less is obtained. Ester interchange of fats and oils in ester mixed oil is carried out with lower alkyl alcohol, when adjusting the quantity of alkali catalyst within a range of 0.1-1 mass parts according to acid value with respect to 100 mass parts of ester mixed oil. Soap by-produced at transesterification process is decomposed with an acid at pH of 2-5, and fatty acid is obtained. The obtained fatty acid is returned at the side of front stage of esterification process, or esterification process. Fatty acid lower alkyl ester is distilled from oil phase obtained at transesterification process by vacuum distillation. Thus, manufacture of fatty acid lower alkyl ester is enabled.    DESCRIPTION OF DRAWING(S) - The figure shows the schematic view of process drawing explaining the manufacturing method of fatty acid lower alkyl ester. (Drawing includes non-English language text)