1. (I) A method for producing an antibody or an antibody fragment thereof, comprising introducing an expression vector which comprises a gene fragment comprising a DNA encoding an antibody or an antibody fragment thereof and a selectable marker gene, and transposon sequences at both terminals of the gene fragment, into a suspension mammalian cell; integrating the gene fragment inserted between a pair of the transposon sequences, into a chromosome of the mammalian cell to obtain a mammalian cell capable of expressing the antibody or the antibody fragment thereof; and suspension-culturing the mammalian cell; (II) a method for producing an antibody or an antibody fragment thereof, which comprises the following steps (A) to (C): (A) a step of simultaneously introducing the following expression vectors (a) and (b) into a suspension mammalian cell (a) an expression vector which comprises a gene fragment comprising a DNA encoding an antibody or an antibody fragment thereof, and transposon sequences at both terminals of the gene fragment, (b) an expression vector which comprises a DNA encoding a transposase which recognizes the transposon sequences and has activity of transferring the gene fragment inserted between a pair of the transposon sequences into a chromosome, (B) a step of transiently expressing the transposase from the expression vector introduced in step (A) to integrate the gene fragment inserted between a pair of the transposon sequences into a chromosome of the mammalian cell, to obtain a suspension mammalian cell capable of expressing the antibody or the antibody fragment thereof, and (C) a step of suspension-culturing the suspension mammalian cell capable of expressing the antibody or the antibody fragment thereof obtained in step (B) to produce the antibody or the antibody fragment thereof; or (III) a method for obtaining a suspension mammalian cell capable of expressing an antibody or an antibody fragment thereof, comprising introducing an expression vector which comprises a gene fragment comprising a DNA encoding an antibody or an antibody fragment thereof and a selectable marker gene, and transposon sequences at both terminals of the gene fragment, into a suspension mammalian cell; and integrating the gene fragment inserted between a pair of the transposon sequences, into a chromosome of the mammalian cell, wherein in the methods of (I)-(III), a pair of the transposon sequences are nucleotide sequences derived from a pair of Tol1 transposons or nucleotide sequences derived from a pair of Tol2 transposons and the suspension mammalian cell is at least one selected from a suspension CHO cell in which a CHO cell is adapted to suspension culture, a PER.C6 cell, a rat myeloma cell YB2/3HL.P2.G11.16Ag.20 (or also called YB2/0) and a suspension mouse myeloma cell NSO adapted to suspension-culture.