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Eigenvalue decomposition for real symmetric matrix is significant in mathematics and engineering. In engineering implementation, most of implementation for eigenvalue decomposition based on hardware prefers to choose Jacobi algorithm because of its inherent parallelism. But the calculated eigenvalue and its corresponding eigenvector from traditional Jacobi algorithm are unordered arrangement. To solve this problem, an improved Jacobi is proposed in this paper, which can get eigenvalue and eigenvector in descending order.