Methods for preparing an ammonium salt and a lithium salt of a fluorinated bis-sulfonylimide by a practical and efficient method with a high yield with a small number of steps. Further, a high purity ammonium salt of a fluorinated bis-sulfonylimide useful for the method for producing a lithium salt is provided.A method for producing a purified particulate solid (II) of a salt represented by the formula (1), which comprises suspending a particulate solid (I) of a salt represented by the formula (1) in a solvent comprising an etheric oxygen atom-containing compound, and separating the solvent by filtration: [HNR3]+[Q1-SO2—N—SO2-Q2]−  (1) wherein each of R's which may be the same or different, is a hydrogen atom or a C1-10 alkyl group, and each of Q1 and Q2 which are independent of each other, is a monovalent fluoroorganic group, or Q1 and Q2 together form a bivalent fluoroorganic group.