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With the dramatic increase in the amount of multimedia data, cross-modal similarity retrieval has become one of the most popular yet challenging problems. Hashing offers a promising solution for large-scale cross-modal data searching by embedding the high-dimensional data into the low-dimensional similarity preserving Hamming space. However, most existing cross-modal hashing usually seeks a semantic representation shared by multiple modalities, which cannot fully preserve and fuse the discriminative modal-specific features and heterogeneous similarity for cross-modal similarity searching. In this paper, we propose a joint specifics and consistency hash learning method for cross-modal retrieval. Specifically, we introduce an asymmetric learning framework to fully exploit the label information for discriminative hash code learning, where 1) each individual modality can be better converted into a meaningful subspace with specific information, 2) multiple subspaces are semantically connected to capture consistent information, and 3) the integration complexity of different subspaces is overcome so that the learned collaborative binary codes can merge the specifics with consistency. Then, we introduce an alternatively iterative optimization to tackle the specifics and consistency hashing learning problem, making it scalable for large-scale cross-modal retrieval. Extensive experiments on five widely used benchmark databases clearly demonstrate the effectiveness and efficiency of our proposed method on both one-cross-one and one-cross-two retrieval tasks.