NOVELTY - Preparing biodiesel by esterification of fatty acid/glyceride of vegetable oil and animal fat involves: (A) contacting vegetable oil/animal fat with mixture of water and organic solvent to form aqueous and organic phase; (B) separating aqueous phase from organic phase; (C) recovering organic solvent of organic phase; (D) contacting organic phase with 1-4C alkyl alcohol (20-60 wt.%) at 120-250 degrees C for 15-90 minutes, in presence of solid heterogeneous catalyst based on magnesium oxide and aluminum trichloride to form mixture of methyl ester and glycerin; and (E) separating methyl ester.    USE - For preparing biodiesel (claimed) useful as an alternative fuel for automotive applications and in static diesel engines for generating electricity.    ADVANTAGE - The purity of the methyl ester and the residual acidity is that required for renewable fuels for use in static diesel engines.    DETAILED DESCRIPTION - A continuous process for the preparation of biodiesel by esterification and/or trans-esterification of fatty acids and/or glycerides contained in vegetable oils and/or animal fats to obtain methyl esters and glycerin involves:    (A) contacting vegetable oils and/or animal fats with a mixture of water and at least one non-polar, aprotic, non-halogenated organic solvent having boiling point below 100 degrees C for 10-90 minutes at 40-120 degrees C to obtain aqueous phase and organic phase;    (B) separation of the aqueous phase from the organic phase;    (C) recovery of the organic solvent of the separated organic phase;    (D) contacting the organic phase with at least one 1-4C alkyl alcohol (20-60 wt.%) at 120-250 degrees C for 15-90 minutes, in the presence of a solid heterogeneous catalyst based on magnesium oxide (MgO) and aluminum trichloride (Al2O3); where the MgO/Al2O3 molar ratio is greater than 4, the catalyst (10-20 vol.%) is suspended in the organic phase to obtain mixture of methyl esters and glycerin; and    (E) separation of the methyl esters from the glycerin of the obtained mixture.