NOVELTY - Water content of fats and oils or used waste oil fat is reduced. The resulting material is reacted with bottom alcohol in presence of a catalyst, and reaction product is separated into fatty acid ester layer and glycerin layer. An aqueous solution of processing agent is added to crude ester obtained by separation such that pH is adjusted to 5-8. The crude fatty acid ester is stirred, and fatty acid ester phase and sludge phase are separated. Alcohol is removed, and heated at 180-280 degrees C. Distillation is carried out, and pure fatty acid alkylester is manufactured.    USE - Manufacture of fatty acid alkylester used as oleo chemical raw material and biodiesel fuel.    ADVANTAGE - The fatty acid alkylester having high purity is efficiently and economically manufactured.    DETAILED DESCRIPTION - Water content of fats and oils or used waste oil fat is reduced to predetermined value. The resulting material is reacted with bottom alcohol in the presence of a catalyst, and reaction product is separated into fatty acid ester layer and glycerin layer. An aqueous solution (1-70%) of processing agent obtained by mixing acid chosen from phosphoric acid, phosphorous acid, hypophosphoric acid, hypophosphorous acid, pyrophosphoric acid, metaphosphoric acid, sulfuric acid, pyrosulfuric acid, carbon dioxide gas, hydrochloric acid, acetic acid, formic acid, oxalic acid or their linear monoalkyl type quaternary ammonium salt, and compound chosen from sodium silicate, sodium sulfate, calcium chloride, zinc chloride and diphenyl phosphate is added to crude ester obtained by separation process in weight ratio of 1-1:10 such that pH is adjusted to 5-8. The crude fatty acid ester is stirred, and fatty acid ester phase and sludge phase are separated. Alcohol is removed, and then heated at 180-280 degrees C and 15 torr or less. Distillation is carried out, and pure fatty acid alkylester is manufactured. An INDEPENDENT CLAIM is included for manufacturing apparatus of fatty acid alkylester, which has an airtight container (A) having opening for injecting fats and oil, opening for injecting catalyst solution, opening for injecting processing agent, outlet for discharging liquid material, discharge port for discharging gas and heating unit (B), stirring unit (M) and air evacuation unit for maintaining pressure reduction state.    DESCRIPTION OF DRAWING(S) - The drawing shows the block diagram of manufacturing apparatus of fatty acid alkylester. (Drawing includes non-English language text)    Airtight container (A)    Heating unit (B)    Circulation pump (D)    Condenser (E)    Stirring unit (M)