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This paper designs an efficient image hashing with a ring partition and a nonnegative matrix factorization (NMF), which has both the rotation robustness and good discriminative capability. The key contribution is a novel construction of rotation-invariant secondary image, which is used for the first time in image hashing and helps to make image hash resistant to rotation. In addition, NMF coefficients are approximately linearly changed by content-preserving manipulations, so as to measure hash similarity with correlation coefficient. We conduct experiments for illustrating the efficiency with 346 images. Our experiments show that the proposed hashing is robust against content-preserving operations, such as image rotation, JPEG compression, watermark embedding, Gaussian low-pass filtering, gamma correction, brightness adjustment, contrast adjustment, and image scaling. Receiver operating characteristics (ROC) curve comparisons are also conducted with the state-of-the-art algorithms, and demonstrate that the proposed hashing is much better than all these algorithms in classification performances with respect to robustness and discrimination.