20 ILCS 105/7.04

The Representative and Senate members of the Council shall serve on the Council for a term of 2 years and may be reappointed by the legislative leader having the right of appointment under Section 7.01 for one or more additional 2 year terms, except that a legislative member's appointment shall be terminated upon his or her leaving the General Assembly. Legislative vacancies shall be filled by the legislative leader having the right of appointment under Section 7.01. A legislative member appointed to fill a vacancy occurring prior to the expiration of the term for which his or her predecessor was appointed shall be appointed for the remainder of such term.