NOVELTY - Preparing purified biodiesel from glycerides comprises e.g. (A) (a) reacting glycerides with at least one alcohol in a transesterification reaction to produce a fatty acid alkyl ester stream, (b) purifying the fatty acid alkyl ester stream by reactive distillation, where the reactive distillation involves separating fatty acid alkyl esters from glycerin and unreacted alcohol while simultaneously reacting glycerin with fatty acids to produce glycerides, and (c) producing purified biodiesel.    USE - The process is useful preparing purified biodiesel from glycerides.    ADVANTAGE - The process do not require high pressures or acid catalysis. The process do not employ toxic co-solvents or water for the extraction of impurities, hence the process provides high yield of biodiesel and inexpensive feedstocks. The process converts low-value, high free fatty acid (FFA) feedstocks to biodiesel with high quality glycerin at a market price as compared to petroleum derived diesel fuels. The process minimizes waste streams during normal operations, by the usage lower operating temperatures and pressures than other commercial biodiesel processes, and the non-usage of toxic co-solvents, hence the process produces high quality glycerin byproduct.    DETAILED DESCRIPTION - Preparing purified biodiesel from glycerides comprises: (A) either (a) reacting glycerides with at least one alcohol in a transesterification reaction to produce a fatty acid alkyl ester stream, (b) purifying the fatty acid alkyl ester stream by reactive distillation, where the reactive distillation involves separating fatty acid alkyl esters from glycerin and unreacted alcohol while simultaneously reacting glycerin with fatty acids to produce glycerides, and (c) producing purified biodiesel; or (B) (a1) reacting glycerides with at least one alcohol in a transesterification reaction to produce a transesterification effluent stream of fatty acid esters and glycerin, (b1) separating the transesterification effluent stream into a fatty acid ester rich stream and a glycerin rich stream, (c1) introducing an organic acid to at least one of transesterification effluent stream, and glycerin rich stream; and (d1) recovering biodiesel