In a multi-way contingency table, a loglinear model can represent various models including a variety of independence models. In this chapter, we consider a goodness-of-fit test for a loglinear model of a multi-way contingency table. In order to improve the accuracy of the approximation of a distribution of a test statistic when the sample size is not so large, we consider an approximation based on an asymptotic expansion for which the amount of computation is not large. We derive an expression to approximate the distribution of the log likelihood ratio (LR) test statistic for a loglinear model based on an asymptotic expansion. Using this expression, we constructed a transformed statistic based on Bartlett adjustment. The transformed statistic converges to a chi-square limiting distribution faster than the original statistic does. By the Monte Carlo simulation, the speed of convergence and the power of the transformed statistic are compared with those of the original one.