The State Labor Relations Board is composed of three (3) members appointed by the Governor, one (1) for a term of two (2) years, one (1) for a term of three (3) years, and one (1) for a term of four (4) years. The Governor shall designate one (1) member to serve as chairman of the board. Thereafter, upon the expiration of the term of any member, members shall be appointed for four (4) year terms by the Governor.