NOVELTY - Increasing fatty acid alkyl ester yield from a feedstock containing free fatty acids, comprises (a) reacting the feedstock in a glycerolysis reactor with glycerin to produce glycerides and water, where the glycerolysis reaction is conducted at a temperature and a pressure for turning the water into water vapor, (b) removing the water vapor from the glycerolysis reactor, and (c) reacting the glycerides in a transesterification reactor with an alcohol to produce fatty acid alkyl esters.    USE - The process is useful for increasing fatty acid alkyl ester yield from a feedstock containing free fatty acids (claimed) for producing biodiesel for diesel engines.    ADVANTAGE - The process is capable of simply and economically producing the biodiesel with high yield, quality, purity and efficiency and without using toxic co-solvents or water for the extraction of impurities.    DETAILED DESCRIPTION - Increasing fatty acid alkyl ester yield from a feedstock containing free fatty acids comprises: either (a) reacting the feedstock in a glycerolysis reactor with glycerin to produce glycerides and water, where the glycerolysis reaction is conducted at a temperature and a pressure for turning the water into water vapor, (b) removing the water vapor from the glycerolysis reactor, and (c) reacting the glycerides in a transesterification reactor with an alcohol to produce fatty acid alkyl esters; or the steps (a) and (b) as above per se, separating the vapor stream into a first fraction and a second fraction, where the second fraction has a high concentration of water, returning the first fraction to the glycerolysis reactor for further processing, and the step (c) as above per se; or the step (a) as above per se, removing a vapor stream from the glycerolysis reactor, recovering from the vapor stream a feedstock rich stream, a glycerin rich stream and a water rich stream, returning at least a portion of the feedstock rich stream to the glycerolysis reactor for further processing, and the step (c) as above per se, where the vapor stream comprises water, feedstock and glycerin; or the steps (a)-(d) as above per se, and processing the glycerides in a transesterification process with an alcohol to produce fatty acid alkyl esters. An INDEPENDENT CLAIM is included for the product produced by the process.