A method of manufacturing a composition of alcohol esters of linear monocarboxylic acids with 6 to 26 carbon atoms from a vegetable or animal oil, neutral or acid, virgin or recycled, with monoalcohols having 1 to 18 carbon atoms, in the presence of a phosphate type catalyst or of an organophosphorous compound of a metal selected from the group made up of zirconium, hafnium and titanium, allows to directly produce, in one or more stages, an ester that can be used as fuel and a pure glycerin.