Bispecific antibodies, while showing great therapeutic potential, pose formidable challenges with respect to their assembly, stability, immunogenicity, and pharmacodynamics. Here we describe a novel class of bispecific antibodies with native human immunoglobulin format. The design exploits differences in the affinities of the immunoglobulin isotypes for Protein A, allowing efficient large-scale purification. Using this format, we generated a bispecific antibody, REGN1979, targeting the B cell marker, CD20, and the CD3 component of the T cell receptor, which triggers redirected killing of B cells. In mice, this antibody prevented growth of B cell tumors and also caused regression of large established tumors. In cynomolgus monkeys, low doses of REGN1979 caused prolonged depletion of B cells in peripheral blood with a serum half-life of approximately 14 days. Further, the antibody induced a deeper depletion of B cells in lymphoid organs than rituximab. This format has broad applicability for development of clinical bispecific antibodies.