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Hashing is a promising approach for compact storage and efficient retrieval of big data. Compared to the conventional hashing methods using handcrafted features, emerging deep hashing approaches employ deep neural networks to learn both feature representations and hash functions, which have been proven to be more powerful and robust in real-world applications. Currently, most of the existing deep hashing methods construct pairwise or triplet-wise constraints to obtain similar binary codes between a pair of similar data points or relatively similar binary codes within a triplet. However, we argue that some critical local structures have not been fully exploited. So, this paper proposes a novel deep hashing method named local semantic-aware deep hashing with Hamming-isometric quantization (LSDH), aiming to make full use of local similarity in hash function learning. Specifically, the potential semantic relation is exploited to robustly preserve local similarity of data in the Hamming space. In addition to reducing the error introduced by binary quantizing, a Hamming-isometric objective is designed to maximize the consistency of similarity between the pairwise binary-like features and corresponding binary codes pair, which is shown to be able to improve the quality of binary codes. Extensive experimental results on several benchmark datasets, including three single-label datasets and one multi-label dataset, demonstrate that the proposed LSDH achieves better performance than the latest state-of-the-art hashing methods.