NOVELTY - Methane-fermentation method, involves (a) performing methane fermentation of organic waste (BB) containing fat in a methane-fermentation tank, (b) removing predetermined amount of fermented liquor from the tank, (c) returning one part of the highly concentrated sludge liquid to the tank and discharging one part of low concentrated sludge liquid out of the tank, (d) mixing highly concentrated sludge liquid with the organic waste, (e) heating the mixture, and (f) performing methane fermentation treatment of saturated fatty acids in the dispersed fats.    USE - The methane-fermentation method is useful for decomposing organic wastes containing fats (claimed).    ADVANTAGE - The method is rapid, stable for a long time, and effective even if the input rate of the dispersed fats is high as the decomposition of the fat in the organic waste is improved by the above-mentioned heating process. The method enables the fat to contact with the methane fermentation bacteria easily, and carries out fat dispersion even if the bacteria extinct at the time of heating and fermentation temperature is less than melting point of the fats.    DETAILED DESCRIPTION - Methane-fermentation method, involves (a) performing methane fermentation of organic waste containing fat in a methane-fermentation tank, (b) removing predetermined amount of fermented liquor from the tank and increasing the sedimentation of sludge liquid, where the sludge concentration is pulled downwards by gravity sedimentation process, (c) returning at least one part of highly concentrated sludge liquid at the side of the lower layer of the sludge sedimentation liquid to the tank and discharging at least one part of low concentrated sludge liquid at the side of the upper layer of the sludge sedimentation liquid out of the tank, (d) mixing highly concentrated sludge liquid with the organic waste, (e) heating the mixture beyond melting point of the fat contained in mixture for fat dispersion, and (f) performing methane fermentation treatment of saturated fatty acids in the dispersed fats by introducing dispersed fats to the tank at a input rate of 0.2 g/l/day or more.    DESCRIPTION OF DRAWING(S) - The drawing shows block diagram of methane-fermentation apparatus (Drawing includes non-English language text) .    Extraction of biogas (AA)    Organic waste (BB)    Waste liquid (CC)