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In many wireless communications/radar applications, constant modulus sequences with low correlation sidelobes levels are desired. In this letter, we present an efficient optimization method to design them. Firstly, we formulate a fourth-order polynomial, but unconstrained, minimization problem. And then, a customized LBFGS (Limited-Memory Broyden Fletcher Goldfarb and Shanno) iterative algorithm is proposed to solve it approximately. Numerical examples show that the proposed approach compares favorably with the state-of-the-art approach.