TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Components: The concentration of phosphorus atoms in phosphorus and phosphorus compounds contained in the reaction raw material is less than 2.5 ppm, and the concentration of calcium atoms in calcium and calcium compounds contained in the reaction raw material is less than 1 ppm.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Method: At least two stages of pressures that are different from each other are applied in the first alcohol stripping step, where the first stage of the pressure in the first or second alcohol stripping step is 0.15-1.5 MPa. The method further involves a second reaction step of reacting fat and oil with alcohol over a solid catalyst, where the fat and oil is contained in an upper phase obtained by phase-separating refined products obtained in the first alcohol stripping step; a second alcohol stripping step of evaporating, from a second reaction liquid obtained in the second reaction step, unreacted alcohol that remains without reacting in the second reaction step; an alcohol refining step for refining alcohol from the unreacted alcohol evaporated in the first and second alcohol stripping steps, with use of at least a part of heat of the unreacted alcohol; a first phase-separation step of phase-separating the first reaction liquid obtained in the first reaction step into a first fatty acid alkyl ester phase and a first glycerin phase; a second reaction step of reacting fat and oil contained in the first fatty acid alkyl ester phase with alcohol over a solid catalyst; a third alcohol stripping step of evaporating, from a second reaction liquid obtained in the second reaction step, unreacted alcohol that remains without reacting in the second reaction step, with use of an evaporator including a heat exchanger (where the residence time of heat exchanger is less than or equal to 20 minutes) selected from a thin film evaporator with an agitating rotor, a thin film evaporator with tubes arranged as a bundle, and a thin film evaporator with a centrifugal rotor; a second phase-separation step of phase-separating refined products obtained in the third alcohol stripping step into a second fatty acid alkyl ester phase and a second glycerin phase; a removal step of removing at least one compound (A1) selected from phosphorus, phosphorus compounds, calcium, and calcium compounds contained in a reaction raw material including the fat and oil and the alcohol; a first phase-separation step of phase-separating a refined product into a first fatty acid alkyl ester phase and a first glycerin phase with use of a separation filter, where the refined product is obtained by evaporating the unreacted alcohol from the first reaction liquid in the first alcohol stripping step; a second reaction step of reacting fat and oil contained in the first fatty acid alkyl ester phase with alcohol over a solid catalyst; and a second phase-separation step of phase-separating a second reaction liquid obtained in the second reaction step into a second fatty acid alkyl ester phase and a second glycerin phase with use of a separation filter. In the third alcohol stripping step, the unreacted alcohol that remains without reacting in the first reaction step is further evaporated from the first glycerin phase with use of the evaporator; or in the third alcohol stripping step, the unreacted alcohol that remains without reacting in the second reaction step is evaporated from the second reacting liquid obtained in the second reaction step, and the unreacted alcohol that remains without reacting in the first reaction step is evaporated from the first glycerin phase. A second alcohol stripping step of evaporating unreacted alcohol from the second reaction liquid is performed before the third alcohol stripping step. The first alcohol stripping step is performed before the first phase-separation step. In the third alcohol stripping step, the unreacted alcohol is evaporated in such a manner that the unreacted alcohol accounts for not greater than 0.5 wt% of the refined products obtained in the third alcohol stripping step. The two stages of pressures different from each other are applied in the second alcohol stripping step. A substance that is contained in the alcohol obtained in the alcohol refining step and that is other than the alcohol accounts for not greater than 1000 parts per million (ppm) of all components contained in the alcohol obtained in the alcohol refining step. Preferred Device: The device further comprises a packed device filled with an adsorber for adsorbing at least one compound (A1) contained in a reaction raw material including the fat and oil and the alcohol, where the reactor causing the reaction raw material having passed the packed device to react over a solid catalyst. EXAMPLE - Palm oil (2.5 kg/hour) and methanol (2.5 kg/hour) were continuously flowed with use of a constant flow pump and their temperatures and their pressures were increased up to 200 degrees C and 5 MPa, respectively, by a heat exchanger. These liquids were mixed in presence of manganese titanate (MnTiO3) catalyst and the mixture was continuously flowed downward from the upper part of the first reactor. The reaction liquid obtained in the first reactor was supplied to the first high pressure flash tower. The pressure of the first high pressure flash tower was 0.35 MPa. A heavy liquid continuously extracted from the bottom of the first high pressure flash tower was supplied to the first low pressure flash tower. Unreacted methanol (1.72 kg/hour) continuously extracted from the top of the first high pressure flash tower was supplied to the heat exchanger and heat of the unreacted methanol was recovered with the heat exchanger and the unreacted alcohol was supplied to the alcohol refining tower. Unreacted methanol (0.25 kg/hour) continuously extracted from the top of the first low pressure flash tower was supplied to the heat exchanger for increasing the temperature of methanol used in the first reaction step and heat of the unreacted methanol was recovered in the heat exchanger and then the unreacted methanol was supplied to the alcohol refining tower. The heavy liquid extracted from the bottom of the first low pressure flash tower was supplied to the heat exchanger for increasing the temperature of palm oil used in the first reaction step and heat of the heavy liquid was recovered in the heat exchanger and the heavy liquid was supplied to the first phase separator and subjected to phase-separation. The upper phase (fatty acid alkyl ester phase) extracted from the first phase separator included fatty acid methyl ester (87.1%), triglyceride (2.4%), diglyceride (1.1%), monoglyceride (1.1%), and methanol (5.4%). The lower phase (glycerin phase) included glycerin (58.2%), fatty acid methyl ester (0.3%), monoglyceride (0.4%), and methanol (41.1%). Subsequently, the upper phase (fatty acid alkyl ester phase) (2.67 kg/hour) extracted from the first phase separator and methanol (2.36 kg/hour) were heated up to 200 degrees C and pressured to 5 MPa by a heat exchanger. These liquids were mixed with each other, and continuously flowed downward from the upper part of the second reactor. The reaction liquid obtained in the second reactor was supplied to the second high pressure flash tower. The pressure of the second high pressure flash tower was 0.35 MPa. The heavy liquid continuously extracted from the bottom of the second high pressure flash tower was supplied to the second low pressure flash tower. Unreacted methanol (1.85 kg/hour) continuously extracted from the top of the second high pressure flash tower was supplied to the heat exchanger and heat of the unreacted methanol was recovered in the heat exchanger. The unreacted methanol was supplied to the heat exchanger for increasing the temperature of methanol used in the second reaction step and heat of the unreacted methanol was recovered in the heat exchanger and supplied to the alcohol storage tank. The heavy liquid extracted from the bottom of the second low pressure flash tower and the lower phase (glycerin phase) extracted from the first phase separator were mixed with each other and the mixture was supplied to the alcohol evaporator. The alcohol evaporator was a thin film evaporator. The pressure was 0.034 MPa and the temperature of a heater was 175 degrees C. The unreacted methanol extracted from the top of the alcohol evaporator was supplied to the alcohol refining tower. The heavy liquid extracted from the bottom of the alcohol evaporator was supplied to the heat exchanger for increasing the temperature of the reaction liquid used in the second reaction step (i.e. the upper phase extracted from the first phase separator) and heat of the heavy liquid was recovered in the heat exchanger and the heavy liquid was supplied to the second phase separator and subjected to phase-separation. The upper phase (fatty acid alkyl ester phase) extracted from the second phase separator included fatty acid alkyl ester (99.4%), triglyceride (0.10%), diglyceride (0.06%), monoglyceride (0.41%), and methanol (0.05%). The lower phase (glycerin phase) included glycerin (99.7%) and methanol (0.3%). The yield of fatty acid alkyl ester was 99.5% and the yield of glycerin was 98.9%. Subsequently, in the alcohol refining tower, methanol was refined from unreacted methanol extracted from the tops of the first high pressure flash tower, the first low pressure flash tower, and the alcohol evaporator. All the amount of heat required in the alcohol refining tower was compensated by the quantity of heat of the unreacted methanol extracted from the tops of the first high pressure flash tower and the second high pressure flash tower. Methanol whose water content was 200 parts per million (ppm) was obtained from the top of the alcohol refining tower and was reused as a reaction material.