Disclosed are a recombinant antibody composition which is a human IgG1 antibody, comprises a CH2 domain in which amino acids at positions 276 and 339 indicated by the EU index as in Kabat, et al. are replaced by other amino acids and has more improved complement-dependent cytotoxic activity than an antibody comprising a CH2 domain before the amino acids are replaced; a DNA encoding the antibody molecule or a heavy chain constant region of the antibody molecule contained in the recombinant antibody composition; a transformant obtainable by introducing the DNA into a host cell; a process for producing the recombinant antibody composition using the transformant; and a medicament comprising the recombinant antibody composition as an active ingredient.