NOVELTY - A biodiesel fuel is produced through transesterification of triglyceride by mixing a triglyceride, an alcohol, and a catalyst comprising non-metal containing quat. ammonium hydroxide or non-metal containing quat. phosphonium hydroxide to form a mixture; removing volatile components from the mixture; allowing the remaining mixture to separate into a biodiesel-rich layer and a glycerol-rich layer; and recovering biodiesel produced.    USE - Process of producing biodiesel fuel through transesterification of a triglyceride. The triglyceride is beef tallow, coconut oil, corn oil, cottonseed oil, lard, olive oil, palm oil, palm kernel oil, peanut oil, soybean oil, linseed oil, tang oil, sunflower oil, safflower oil, canola oil, rapeseed oil, sesame oil, babassu oil, Perilla oil, oiticica oil, fish oils, menhaden oil, castor oil, Chinese tallow tree oil, Physic nut oil, Cuphea seed oil, microalgal oils, Jatropha oil, bacterial oils or fungal oils. (All claimed)    ADVANTAGE - The process employs a catalyst having non-metal containing quat. ammonium hydroxide or non-metal containing quat. phosphonium hydroxide thus producing glycerol which is salt-free and that may be sold in a more pure state to a variety of industries; that may be removed from the biodiesel and glycerol products by simple heating and evacuation or by passing through an acidic column thus not requiring any need for neutralization of the catalyst with an acidic solution or washing the products with aqueous solvents to get rid of metal-salt substances; that is highly reactive; having low catalyst levels, quick reaction time, and relatively low reaction temperature; that may be used with or without the use of a cosolvent system; and that is cheap and commercially available.    DETAILED DESCRIPTION - An INDEPENDENT CLAIM is included for a metal-containing salt free catalyst producing biodiesel fuel and glycerol through transesterification when combined with a triglyceride and an alcohol, removing volatile compound from the combination, and allowing remaining mixture to separate into a biodiesel-rich layer and a glycerol-rich layer where the catalyst comprises non-metal containing quat. ammonium hydroxide or non-metal containing quat. phosphonium hydroxide.