A method for continuously refining and esterifying fatty materials, whatever the origin of the raw material (especially designed for animal fats of categories 1 and 2) consists in treating the fatty material with an acid (preferably acetic acid for fats of animal origin and methanesulphonic acid for fats of plant origin), followed by acid esterification in special, multi-stage continuous reactors. The particularity of the claimed method is that esterification can be carried out continuously in two stages, in series or in parallel depending on the degree of acidity of the raw material (two stages in series for more than 50% FFA, and two stages in parallel for less than 50% FFA, no acidity value being limiting). Finally, a third phase is performed for recovering methanol, the dissolved oil phase and an aqueous phase, all of which are re-used. This method allows reducing the free fatty acid and/or impurity content of the original material continuously and without thermal or chemical degradation, for all types of raw material (crude, refined, partially refined,...). This improvement to the method causes an increase in the final yield of biodiesel, besides an improvement in the quality of the product obtained. The inclusion of the method as an additional step in today's biodiesel production technologies, or as an independent step, allows a high-quality liquid biofuel to be obtained for use in diesel engines: i) either as a pure biofuel (B100), ii) mixed with gas oil (biodiesel content > 7%), or iii) as a gas oil additive (mixtures < 7%) from waste (in particular animal fats of categories 1 and 2, vegetable oleins and pure fatty acids), solving the operational problem encountered by most biodiesel production plants and the waste disposal environmental challenge facing governments today (in particular the disposal of animal fats of categories 1 and 2).