Biodiesel, an alternative diesel fuel derived from vegetable oil, animal fats, or waste vegetable oils, is obtained by reacting the oil or fat with monohydric aliphatic alcohols having 1-5 carbon atoms (ester exchange or transesterification) to their esters. Chemically, biodiesel is a fatty acid (m)ethyl ester. Biodiesel plays an important role in meeting future fuel requirements in view of its ability to reduce emissions from diesel engines for many air pollutant precursors, the lower toxicity of the diesel particulate matter emissions, and its edge over conventional diesel as they are obtained from renewable sources. In the supercritical alcohol transesterification method, the yield of conversion raises 50-95% for the first 8 min. In the catalytic supercritical methanol transesterification method, the yield of conversion raises 60-90% for the first minute. The reaction between sodium methoxide in methanol and a vegetable oil is very rapid; for example, they are completely transesterified in 4-6 min at room temperature.