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Person re-identification (re-ID) is an important topic in computer vision. This paper studies the unsupervised setting of re-ID, which does not require any labeled information and thus is freely deployed to new scenarios. There are very few studies under this setting, and one of the best approach till now used iterative clustering and classification, so that unlabeled images are clustered into pseudo classes for a classifier to get trained, and the updated features are used for clustering and so on. This approach suffers two problems, namely, the difficulty of determining the number of clusters, and the hard quantization loss in clustering. In this paper, we follow the iterative training mechanism but discard clustering, since it incurs loss from hard quantization, yet its only product, image-level similarity, can be easily replaced by pairwise computation and a softened classification task. With these improvements, our approach becomes more elegant and is more robust to hyper-parameter changes. Experiments on two image-based and video-based datasets demonstrate state-of-the-art performance under the unsupervised re-ID setting.