An anti-CD20 antibody with an improved characteristic selected from: a slower off-rate slower antigen dissociation rate higher CDC activity higher ADCC activity higher apoptotic activity greater ability to induced cell death in vitro in the absence of cross-linking and greater ability to kill or inhibit the growth of CD20-positive cells in vivo. The antibody is improved by a method that substitutes an amino acid at Kabat position 101 in the third CDR sequence of the heavy chain. The CDR sequences of the unsubstituted antibody are light chain CDR sequences CDRL1 (RASSSVSYIH), CDRL2 (ATSNLAS) and CDRL3 (QQWTSNPPT) and heavy chain CDR sequences CDRH1 (SYNMH), CDRH2 (AIYPGNGDTSYNQKFKG) and CDRH3 (STYYGGDWYFNV). The substitution can be replacing the asparagine at Kabat position 101 with aspartate. The antibody can be veltuzumab. The antibody can be used for treating B-cell mediated immune disease, autoimmune disease, B-cell lymphoma and leukaemia, graft-versus-host-disease (GVHD), organ transplant rejection, immune haemolytic anaemia, allosensitisation and cryoglobulinaemia.