  In [H. Suzuki, Association schemes with multiple $Q$-polynomial structures,
J. Algebraic Combin. 7 (1998) 181-196], Suzuki gave a classification of
association schemes with multiple $Q$-polynomial structures, allowing for one
exceptional case which has five classes. In this paper, we rule out the
existence of this case. Hence Suzuki's theorem mirrors exactly the well-known
counterpart for association schemes with multiple $P$-polynomial structures, a
result due to Eiichi Bannai and Etsuko Bannai in 1980.
