A variant of a polypeptide comprising a human IgG Fc region is described, which variant comprises an amino acid substitution at one or more of amino acid positions 270, 322, 326, 327, 329, 331, 333 or 334 of the human IgG Fc region. Such variants display altered effector function. For example, C1q binding and/or complement dependent cytotoxicity (CDC) activity may be altered in the variant polypeptide. The application also discloses a variant of a parent polypeptide comprising a human IgG Fc region, which variant has a better binding affinity for human C1q than the parent polypeptide.