A method for producing a fluoroalkanesulfonic anhydride represented by the following general formula by introducing a fluoroalkanesulfonic acid represented by the following formula and diphosphorus pentoxide into a kneader-type reactor having a maximum power of 1.0 kW or greater per an actual capacity of 100 L and equipped with at least two-shaft blades and by kneading them in the reactor by a power of 0.5 kW or greater per an actual capacity of 100 L, the method comprising: a first step of introducing the fluoroalkanesulfonic acid and diphosphorus pentoxide into the reactor such that a molar ratio of a total amount of the fluoroalkanesulfonic acid introduced to a total amount of the diphosphorus pentoxide introduced becomes 2.0 or greater; a second step in which the fluoroalkanesulfonic acid is reacted with the diphosphorus pentoxide, while kneading the fluoroalkanesulfonic acid and the diphosphorus pentoxide, which have been introduced in the first step, at a temperature in the reactor that is 40 °C or higher and is lower than 100 °C, to produce the fluoroalkanesulfonic anhydride as a main product and metaphosphoric acid as a by-product, and in which the fluoroalkanesulfonic anhydride as the main product is discharged from the reactor; a third step of discharging the unreacted fluoroalkanesulfonic acid from the reactor, while further kneading a residue in the reactor, which is obtained by the second step, at a temperature in the reactor that is 100 °C or higher and is lower than 140 °C, a fourth step of adding orthophosphoric acid to a residue in the reactor, which is obtained by the third step, to conduct a reaction with the metaphosphoric acid, thereby synthesizing pyrophosphoric acid; and a fifth step of discharging a residue containing the pyrophosphoric acid, which has been synthesized by the fourth step, from the reactor wherein the method is characterized by that the unreacted fluoroalkanesulfonic acid, which is discharged by the third step, is used as a total or part of the fluoroalkanesulfonic acid introduced in the first step, R f SO 3 H ··· (R f SO 2) 2 O ··· wherein R f represents a C 1-4 straight-chain or C 3-4 branched chain, saturated or unsaturated, fluoroalkyl group. a first step of introducing the fluoroalkanesulfonic acid and diphosphorus pentoxide into the reactor such that a molar ratio of a total amount of the fluoroalkanesulfonic acid introduced to a total amount of the diphosphorus pentoxide introduced becomes 2.0 or greater; a second step in which the fluoroalkanesulfonic acid is reacted with the diphosphorus pentoxide, while kneading the fluoroalkanesulfonic acid and the diphosphorus pentoxide, which have been introduced in the first step, at a temperature in the reactor that is 40 °C or higher and is lower than 100 °C, to produce the fluoroalkanesulfonic anhydride as a main product and metaphosphoric acid as a by-product, and in which the fluoroalkanesulfonic anhydride as the main product is discharged from the reactor; a third step of discharging the unreacted fluoroalkanesulfonic acid from the reactor, while further kneading a residue in the reactor, which is obtained by the second step, at a temperature in the reactor that is 100 °C or higher and is lower than 140 °C, a fourth step of adding orthophosphoric acid to a residue in the reactor, which is obtained by the third step, to conduct a reaction with the metaphosphoric acid, thereby synthesizing pyrophosphoric acid; and a fifth step of discharging a residue containing the pyrophosphoric acid, which has been synthesized by the fourth step, from the reactor