Since an IgG antibody has two antigen-binding fragments (Fab) both of which link to an Fc region, there had long been a concept of an asymmetric bispecific IgG antibody capable of binding to two different antigens or epitopes. The asymmetric reengineering technology immunoglobulin (ART-Ig) is a humanized asymmetric bispecific IgG antibody. An asymmetric bispecific IgG antibody typically has 2 kinds of heavy chain and 2 kinds of light chain. If the 4 chains were simultaneously expressed in a recombinant cell to produce the desired asymmetric bispecific IgG antibody, as many as 9 kinds of unwanted byproduct IgG molecules would also be assembled and secreted. A method of reducing the byproduct IgG molecules using a common light chain in the asymmetric bispecific IgG antibody and also by introducing “knobs-into-holes” mutations in its Fc region to prioritize a specific hetero-dimerization of the heavy chains.