Polymer conjugates containing a C1-inhibitor having at least one substantially non-antigenic polymer covalently attached to the C1-inhibitor via thiol group of the C1 inhibitor is provided. In the polymer conjugates of the present invention, the substantially non-antigenic polymer is attached to either free thiol from a cysteine of thiol generated from disulfide bonds in C1 inhibitor. Alternatively, the substantially non-antigenic polymer is attached to one of more thiols in C1 inhibitor via bifunctional spacer. In addition, methods of making the conjugates as well as methods of treatment using the conjugate of the present invention are also provided.
