NOVELTY - A fatty-acid alkyl ester (4) is obtained by esterification using a column type counter flow reactor (30) provided with trays (34a-34d) installed in a horizontal direction such that compartments are formed, and openings formed on the trays. Fatty-acid raw material (1) is introduced at the top and alcohol (2) is introduced at the bottom of the reactor, and esterification reaction is carried out in each tray under countercurrent conditions at 200350 degrees C and 135 bar.    USE - Manufacture of fatty-acid alkyl ester e.g. fatty-acid methyl ester for use as biodiesel.    ADVANTAGE - The method eliminates the need for glycerin purification, provides excellent conversion rate with respect to fatty acid, and enables simple and economical manufacture of high-quality fatty-acid alkyl ester. Since the process is non-catalytic, the need for neutralization, filtration, and washing for removing catalyst is eliminated. Surplus alcohol which is not esterified can be collected and reused.    DETAILED DESCRIPTION - A fatty-acid alkyl ester is obtained by esterification using a column type counter flow reactor provided with trays installed in a horizontal direction such that compartments are formed in a vertical direction in the reactor, and openings formed on the trays to connect neighboring trays vertically such that the openings of neighboring trays are formed to cross one another. Fatty-acid raw material is introduced at the top and alcohol is introduced at the bottom of the reactor, and esterification reaction is carried out in each tray under countercurrent conditions at 200350 degrees C and 135 bar. An INDEPENDENT CLAIM is included for apparatus for manufacturing fatty-acid alkyl ester.    DESCRIPTION OF DRAWING(S) - The drawing shows a schematic view of the column-type counter flow reactor. (Drawing includes non-English language text)    Fatty-acid raw material (1)    Alcohol (2)    Fatty-acid alkyl ester (4)    Column-type counter flow reactor (30)    Trays (34a-34d)