For many of the classical association schemes, there are specific sets of orthogonal polynomials associated with them. When these can be found explicitly, the polynomials can be given as hypergeometric or basic hypergeometric series. A new association scheme was constructed by \textit{A. A. Ivanov}, \textit{M. E. Muzichuk} and \textit{V. A. Ustimenko} [Eur. J. Comb. 10, No. 4, 337-345 (1989; Zbl 0709.05015)], and the polynomials associated with the new scheme are kernel polynomials of those for the original scheme. The author determines all the cases where the polynomials of a classical association scheme are the kernel polynomials of the polynomials associated to another classical scheme.