Abstract: A mixture of fatty acids or their esters derived from natural oils and fats including eicosapentaenoic acids or their derivatives is precision distilled under a high vacuum using a plurality of distillation columns, three distillation columns or more in particular, in order to acquire a fraction consisting mainly of fatty acids of carbon number 20 or their esters, which is then subjected to a column chromatography with a reversed-phase distribution system. Eicosapentaenoic acids or their esters, which is useful for preventing or treating thrombus, with a purity as high as 99% and above and with a recovery rate 55% or above, is produced.