Categorical data composed of qualitative valued attributes are ubiquitous in machine learning tasks. Due to the lack of well-defined metric space, categorical data distributions are difficult to be intuitively understood. Clustering is a popular data analysis technique suitable for data distribution understanding. However, the success of clustering often relies on reasonable distance metrics, which happens to be what categorical data naturally lack. This paper therefore introduces a new finding that the order relation among attribute values is the decisive factor in clustering accuracy, and is also the key to understanding categorical data clusters, because the essence of clustering is to order the clusters in terms of their admission to samples. To obtain the orders, we propose a new learning paradigm that allows joint learning of clusters and the orders. It alternatively partitions the data into clusters based on the distance metric built upon the orders and estimates the most likely orders according to the clusters. The algorithm achieves superior clustering accuracy with a convergence guarantee, and the learned orders facilitate the understanding of the non-intuitive cluster distribution of categorical data. Extensive experiments with ablation studies, statistical evidence, and case studies have validated the new insight into the importance of value order and the method proposition. The source code is temporarily opened in https://anonymous.4open.science/r/OCL-demo.

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