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In practice, many medical datasets have an underlying taxonomy defined over the disease label space. However, existing classification algorithms for medical diagnoses often assume semantically independent labels. In this study, we aim to leverage class hierarchy with deep learning algorithms for more accurate and reliable skin lesion recognition. We propose a hyperbolic network to learn image embeddings and class prototypes jointly. The hyperbola provably provides a space for modeling hierarchical relations better than Euclidean geometry. Meanwhile, we restrict the distribution of hyperbolic prototypes with a distance matrix that is encoded from the class hierarchy. Accordingly, the learned prototypes preserve the semantic class relations in the embedding space and we can predict the label of an image by assigning its feature to the nearest hyperbolic class prototype. We use an in-house skin lesion dataset which consists of around 230k dermoscopic images on 65 skin diseases to verify our method. Extensive experiments provide evidence that our model can achieve higher accuracy with less severe classification errors than models without considering class relations.