TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Process: The catalyst introduces sulfonic acid group to resin microparticles, during esterification. The ratio of alcohol with respect to 100 parts weight of fats-and-oils is 10-80 parts weight, during esterification and/or transesterification. The resin foam adsorbed with impurity is subjected to alcohol wash, and further subjected to esterification and/or transesterification.Preferred Catalyst: The average particle diameter of esterification catalyst microparticles is 0.1-100 microns. The transesterification catalyst microparticles consist of hydroxide, oxide, complex oxide and carbonate of alcohol-insoluble alkaline-earth metal and/or alkali metal immobilized by alcohol insoluble solid.    TECHNOLOGY FOCUS - POLYMERS - Preferred Foam: The resin foam has specific gravity of 0.005-0.2, and is hydrophilic and basic resin foam having a continuous pore. The resin foam consisting of a cross-linkable resin having benzene ring by which it is modified to be strongly acidic, is sulfonated. The resin foam is preferably melamine-resin foam in which catalyst microparticles are supported through organic-acid property microparticles and/or inorganic acidic microparticles. The average particle diameter of catalyst microparticles, organic-acid property microparticles and inorganic acidic microparticles is 0.1-10 microns, 0.1-100 microns and 10-100 nm, respectively. EXAMPLE - (In g) Strong acid-type ion exchange resin was ground, and strongly acidic microparticles (20) was obtained. The obtained microparticles were added to methanol (100 ml), and catalyst minute particle dispersion was obtained. The obtained dispersion liquid (20 ml) was added to melamine resin foam having porosity of 99%, filtered and dried to obtain catalyst-supported melamine resin foam. The obtained resin foam was filled in a column. A raw material containing waste edible oil with free fatty acid (1.8 wt.%), was supplied to the column at 20 g/hour. Methanol was supplied at 2.6 g/hour, and esterification was carried out. The obtained reaction liquid was subjected to transesterification and purification to obtain highly pure fatty-acid alkylester.