NOVELTY - The method comprises transesterifying (16) fats and oils (12) with a lower alcohol (14) e.g. methyl alcohol using a non-oxidizing catalyst such as potassium hydroxide to produce a fatty acid alkyl ester, refining (18) the fatty acid alkyl ester, heating the refined fatty acid alky ester to fuse the refined fatty acid alky ester, mixing (22) the fused fatty acid alkyl ester with light oil (20) to produce a mixed solution, and removing solids and/or water from the fats and oils by gravity separation. The heating step comprises heating the refined fatty acid alkyl ester to a temperature.    USE - Method for producing biodiesel fuel from fats and oils, where the biodiesel fuel is useful for a fuel of an internal engine.    ADVANTAGE - The method is capable of effectively producing the environmentally friendly biodiesel fuel thus reliably using the biodiesel fuel as a fuel without causing any clogging in an engine filter.    DETAILED DESCRIPTION - The method comprises transesterifying (16) fats and oils (12) with a lower alcohol (14) e.g. methyl alcohol using a non-oxidizing catalyst such as potassium hydroxide to produce a fatty acid alkyl ester, refining (18) the fatty acid alkyl ester, heating the refined fatty acid alky ester to fuse the refined fatty acid alky ester, mixing (22) the fused fatty acid alkyl ester with light oil (20) to produce a mixed solution, and removing solids and/or water from the fats and oils by gravity separation. The heating step comprises heating the refined fatty acid alkyl ester to a temperature such that a temperature of the mixed solution during mixing step is equal to or higher than its cold filter plugging point but lower than a temperature, at which unsaturated fatty acids contained in the fused fatty acid alkyl ester are oxidized. The mixing step is subdivided into multiple steps and performed at substantially or nearly an ambient temperature step-by-step. The heating step is performed under a sealed condition to block air and/or light. The fats and oils is a material selected from plants and animals, and is palm oil. The refining step comprises filling a container with the refined fatty acid alkyl ester and storing the refined fatty acid alkyl ester in solid form within the container under a sealed condition, and the heating step comprises heating the solid fatty acid alkyl ester from outside the container while the container is sealed to fuse the solid fatty acid alkyl ester.    DESCRIPTION OF DRAWING(S) - The diagram shows a schematic view of a process, in which the biodiesel fuel is produced by a method (Drawing includes non-English language text).    Fats and oils (12)    Lower alcohol (14)    Transesterification reaction step of transesterifying fats and oils with lower alcohol (16)    Fuel refining step of refining fatty acid alkyl ester produced in the transesterification reaction step (18)    Light oil (20)    Mixing step of mixing fatty acid alkyl ester refined in the fuel refining step with light oil. (22)