<p>A transesterification process for producing fatty acid methyl ester comprising the steps of reacting oil of plant or animal origin with methanol premixed with an alkaline catalyst in aqueous form at a temperature of 600C to 700C to produce a first reaction products; withdrawing formed glycerol continuously from the first reaction products; reacting additional methanol premixed with the alkaline catalysts into first reaction products by stirring when conversion of fatty acid methyl ester in the first reaction products reached at least 90% to acquire the fatty acid methyl ester with a conversion rate of at least 99%, wherein the alkaline catalyst is dissolved in water with a concentration of 40% to 50%.</p>