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Hashing plays an important role in information retrieval, due to its low storage and high speed of processing. Among the techniques available in the literature, multi-modal hashing, which can encode heterogeneous multi-modal features into compact hash codes, has received particular attention. Most of the existing multi-modal hashing methods adopt the fixed weighting factors to fuse multiple modalities for any query data, which cannot capture the variation of different queries. Besides, many methods introduce hyper-parameters to balance many regularization terms that make the optimization harder. Meanwhile, it is time-consuming and labor-intensive to set proper parameter values. The limitations may significantly hinder their promotion in real applications. In this paper, we propose a simple, yet effective method that is inspired by the Hadamard matrix. The proposed method captures the multi-modal feature information in an adaptive manner and preserves the discriminative semantic information in the hash codes. Our framework is flexible and involves a very few hyper-parameters. Extensive experimental results show the method is effective and achieves superior performance compared to state-of-the-art algorithms.