TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: The esterification catalyst is freed by the evaporation of methanol and water and re-used for the transesterification process. The esterification catalyst after evaporating excess used methanol is introduced into a rectification column containing a residual water content of less than 0.1%, and used again for the esterification process. The triglyceride-methyl ester mixture obtained after the esterification and phase separation process is preferably three times washed with methanol. The washing takes place using sequentially connected mixer/settler apparatus or a countercurrent column. The esterification reaction takes place in the vicinity of the boiling point of the methanol and under depressurized atmosphere. In the process, a basic catalyzed transesterification with methanol is introduced into the esterified mixture of fatty acid triglycerides and fatty acid methyl ester. The basic catalyzed transesterification takes place with an esterified mixture of fatty acid triglyceride and fatty acid methyl ester using sodium methylate (as catalyst), where the acid number of the fatty acid is less than 0.4 mg potassium hydroxide/g. The process is batchwise or continuous process. Preferred Components: The homogeneous acid catalyst is ethane-1,2-disulfonic acid, benzene-1,3-disulfonic acid or naphthalene-1,5-disulfonic acid. The lower alcohol is methanol. The fatty acids contained in fatty acid triglycerides or fatty acid methyl esters are oils and fats of plant origin, which are extracted e.g. by pressing or extracting particular rapeseed, sunflower seeds, soybeans, jatropha, palm fruits, maize germ or cottonseed, and using 1-2%, sometimes greater than or equal to 15% of free fatty acids, after degumming, where the fatty acid contained triglyceride is from waste fats, which are obtained from: the food preparation containing 3-6% free fatty acids, in some cases containing large amount of free fatty acids; oil fractions from distillation of crude oil or chemical de-acidification of the soap stock (split fatty acids); oil phases containing 40-90% free fatty acids, occasionally up to 100%, which by neutralization of the alkali-catalyzed transesterification of oils with methanol provides glycerol phase as a by-product; or fatty acid methyl ester containing 20-80% of free fatty acids. In the fatty acid triglycerides, greater than 30% of free fatty acids are mixed with triglycerides containing less than 30% of free fatty acids, thus the percentage of fatty acids in the total amount is 30%, which does not exceed the triglyceride. The carrier materials for the catalyst are glycerin or diethylene glycol. EXAMPLE - Raw, roughly degummed rapeseed oil (130 g) containing free fatty acid (15%) and phosphorus (maximum 50 ppm) was transesterified with oil phase (20 g) containing free fatty acids (12 g) and fatty acid methyl ester (8 g) to obtain glycerol phase containing a mixture of free fatty acids (9.3%), naphthalen-1,5-disulfonic acid (2 g) and diethylene glycol (8 g). The obtained glycerol phase was dissolved in methanol (45 g) and rapeseed oil phase mixture and intensively agitated for 75 minutes at 60-65 degrees C. Subsequently, the mixture was phase separated to obtain a light phase comprising methanol, diethylene glycol, naphthalene-1,5-disulfonic acid and reaction water, and a heavy phase comprising rapeseed oil and rape methyl ester. The obtained heavy phase (160 g) was three times washed with methanol (18 g) and 30% sodium methylate (1.5 g) in methanol for 30 minutes at 60-65 degrees C and transferred into a separating funnel. After 30 minutes, a mixture of light phase (157 g) and heavy glycerol phase (21 g) was separated. The light phase (157 g) in a second transesterification with additional 30% sodium methylate (0.7 g) was stirred for 20 minutes at 60-65 degrees C, and subsequently added with glycerol phase (8 g), stirred for further 3 minutes and transferred in a separatory funnel. After phase separation, the light phase was washed with hydrochloric acid to remove adhered residual soaps and the excess methanol and water were removed by distillation to obtain rapeseed methyl ester (150 g).