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In this paper, the generation of sequency-ordered complex Hadamard transform (SCHT) based on the complex Rademacher matrices is presented. The exponential form of SCHT is also derived, and the proof for the unitary property of SCHT is given. Using the sparse matrix factorization, the fast and efficient algorithm to compute the SCHT transform is developed, and its computation load is described. Certain properties of the SCHT matrices are derived and analyzed with the discussion of SCHT applications in spectrum analysis and image watermarking. Relations of SCHT with fast Fourier transform (FFT) and unified complex Hadamard transform (UCHT) are discussed.