Abstract The inverse of the dispersion matrix plays an important role in mixed model analysis. Searle and Henderson [J. Amer. Statist. Assoc, 74 (1979) 465] showed that for a general balanced mixed ANOVA model, such an inverse can be expression in the same form as the dispersion matrix, i.e., a linear combination of Kronecker products. However, the coefficients of such a linear combination are given in a way that it is not easy to see what each coefficient is. In this paper, we give explicit expressions for these coefficients. An application of the result is considered.