This article discusses the concept of an invariant item ordering (IIO) for polytomously scored items and proposes methods for investigating an IIO in real test data. Method manifest IIO is proposed for assessing whether item response functions intersect. Coefficient H[superscript T] is defined for polytomously scored items. Given that an IIO holds, coefficient H[superscript T] expresses the accuracy of the item ordering. Method manifest IIO and coefficient H[superscript T] are used together to analyze a real data set. Topics for future research are discussed. (Contains 4 tables and 2 figures.)