Polymer conjugates containing a C1-inhibitor having at least one substantially non-antigenic polymer covalently attached to the C1-inhibitor via amino group of the C1 inhibitor are provided. In the polymer conjugates, the substantially non-antigenic polymer is attached to the N-terminal of C1-inhibitor. Alternatively, the substantially non-antigenic polymer is attached to the N-terminal of C1-inhibitor and at least one more of the substantially non-antigenic polymer is attached to lysine and/or histidine of the C1-inhibitor. Furthermore, the polymer conjugates is attached to C1-inhibitor either via permanent or releasable spacers. In addition, methods of making the conjugates as well as methods of treatment using the conjugate of the present invention are also provided.
