Statistics R a based on power divergence can be used for testing the homogeneity of a product multinomial model. All R a have the same chi-square limiting distribution under the null hypothesis of homogeneity. R 0 is the log likelihood ratio statistic and R 1 is Pearson's X 2 statistic. In this article, we consider improvement of approximation of the distribution of R a under the homogeneity hypothesis. The expression of the asymptotic expansion of distribution of R a under the homogeneity hypothesis is investigated. The expression consists of continuous and discontinuous terms. Using the continuous term of the expression, a new approximation of the distribution of R a is proposed. A moment-corrected type of chi-square approximation is also derived. By numerical comparison, we show that both of the approximations perform much better than that of usual chi-square approximation for the statistics R a when a ≤ 0, which include the log likelihood ratio statistic.