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The bone age, reflecting the degree of development of the bones, can be used to predict the adult height and detect endocrine diseases of children. Both examinations of radiologists and variability of operators have a significant impact on bone age assessment. To decrease human intervention , machine learning algorithms are used to assess the bone age automatically. However, conventional supervised deep-learning methods need pre-labeled data. In this paper, based on the convolutional auto-encoder with constraints (CCAE), an unsupervised deep-learning model proposed in the classification of the fingerprint, we propose this model for the classification of the bone age and baptize it BA-CCAE. In the proposed BA-CCAE model, the key regions of the raw X-ray images of the bone age are encoded, yielding the latent vectors. The K-means clustering algorithm is used to obtain the final classifications by grouping the latent vectors of the bone images. A set of experiments on the Radiological Society of North America pediatric bone age dataset (RSNA) show that the accuracy of classifications at 48-month intervals is 76.15%. Although the accuracy now is lower than most of the existing supervised models, the proposed BA-CCAE model can establish the classification of bone age without any pre-labeled data, and to the best of our knowledge, the proposed BA-CCAE is one of the few trails using the unsupervised deep-learning method for the bone age assessment.