NOVELTY - A fatty-acid ester is obtained by transesterification of fats-and-oils and alcohol, using two or more units (columns) (2-4). While carrying out esterification process by unit(s), regeneration process is carried out by the other unit(s). Esterification involves contacting fats-and-oils and alcohol with an anion exchanger which is insoluble with respect to fats-and-oils, alcohol, and fatty-acid ester. Regeneration process involves substituting the counter-ion of the anion exchanger.    USE - Manufacture of fatty-acid ester for use as biodiesel fuel.    ADVANTAGE - The method enables efficient and continuous manufacture of large quantities of fatty-acid ester, without requiring separation process of product and catalyst, and an apparatus for catalyst regeneration. Reaction and regeneration processes can be carried out without removal of catalyst from the column. Only the catalyst portion whose activity is reduced needs to be regenerated. Since fats-and-oils can be used in high concentration, productivity is high. The anion exchanger has excellent economical efficiency and stable catalytic activity. Even when performance deteriorates, regeneration of exchange group is easy. The time-dependent decreasing rate of catalyst activity is low. The obtained fatty-acid ester can be efficiently used as biodiesel fuel with low environmental impact, and can be mixed with light oil.    DETAILED DESCRIPTION - A fatty-acid ester is obtained by transesterification of fats-and-oils and alcohol, using two or more units which carry out fatty-acid esterification process and anion-exchanger regeneration process. While carrying out esterification process by unit(s), regeneration process is carried out by the other unit(s). The fatty-acid ester is produced continuously by alternately carrying out esterification and regeneration process. Esterification involves contacting fats-and-oils and alcohol with an anion exchanger which is insoluble with respect to fats-and-oils, alcohol, and fatty-acid ester. Regeneration process involves substituting the counter-ion of anion exchanger. An INDEPENDENT CLAIM is included for fatty-acid-ester production apparatus (1) consisting of containers having two or more openings and filled with the anion exchanger, a mechanism controlled to carry out regeneration and esterification processes in turns within each container, and a mechanism for allowing flow of fats-and-oils and alcohol from one opening during esterification reaction, and for allowing flow of produced fatty-acid ester from the other opening.    DESCRIPTION OF DRAWING(S) - The drawing shows an outline diagram of the fatty-acid-ester production apparatus. (Drawing includes non-English language text)    Production apparatus (1)    Columns (2-4)    Substrate tank (5)    Recovery tank (8)    Regeneration bath (17)