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Cross-modal hashing (CMH) models are introduced to significantly reduce the cost of large-scale cross-modal data retrieval systems. In many real-world applications, however, data of new categories arrive continuously, which requires the model has good extensibility. That is the model should be updated to accommodate data of new categories but still retain good performance for the old categories with minimum computation cost. Unfortunately, existing CMH methods fail to satisfy the extensibility requirements. In this work, we propose a novel extensible cross-modal hashing (ECMH) to enable highly efficient and low-cost model extension. Our proposed ECMH has several desired features: 1) it has good forward compatibility, so there is no need to update old hash codes; 2) the ECMH model is extended to support new data categories using only new data by a well-designed ``weak constraint incremental learning'' algorithm, which saves up to 91\% time cost comparing with retraining the model with both new and old data; 3) the extended model achieves high precision and recall on both old and new tasks. Our extensive experiments show the effectiveness of our design.