NOVELTY - Fats are treated with methanol and super acid solid catalyst. The resulting water is separated and removed, and methanol is recirculated. Then super acid solid catalyst is removed by filtration. The filtrate is treated with heterogeneous alkaline catalyst. The catalyst is removed. The glycerine is separated from methyl esters of fatty acids, and is then treated with the heterogeneous alkaline catalyst. The catalyst is removed, and excess methanol is removed by distillation. The glycerine is separated from methyl esters of fatty acids, in order to obtain fatty acid methyl ester.    USE - Manufacture of fatty acid methyl ester used as diesel biofuel.    ADVANTAGE - The method enables economical and energy-efficient manufacture of fatty acid methyl ester, using easily-removable heterogeneous catalyst, without requiring additional operations for the purification of methyl esters, and effectively utilizes byproduct raw glycerine.    DETAILED DESCRIPTION - Fats are treated with 0.308-0.566 wt.% methanol and 4-5 wt.% super acid solid catalyst at 68 plus minus 2 degrees C. The water resulting from din esterification reaction of the fatty acids is separated from methanol in rectification column. Then, the water is removed, and methanol is recirculated, until acidity index of the reaction mass drops at 2 mg potassium hydroxide/g. Then the super acid solid catalyst is removed by filtration, which can be reused. The filtrate is treated with 5-6 wt.% heterogeneous alkaline catalyst at 67 plus minus 2 degrees C for 60-90 minute. The catalyst is removed by filtration or centrifugation. The glycerine is separated from the methyl esters of fatty acids by decantation or centrifugation, and is then treated with the heterogeneous alkaline catalyst separated before at 67 plus minus 2 degrees C for 60-90 minutes. The catalyst is removed by filtration or centrifugation, and excess methanol is removed by distillation. At atmospheric pressure and vacuum conditions, the glycerine is separated from methyl esters of fatty acids by decantation or centrifugation, which is finally filtered through inorganic filtering layer, in order to obtain fatty acid methyl ester. The super solid catalyst is fresh or recovered from previous batches, and is sulfate-titanium dioxide-lanthanum oxide-type catalyst. The ratio of titanium and lanthanum in the super solid catalyst is 30:1.