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In this paper, we propose a new preconditioner for solving linear systems by the preconditioned conjugate gradient (PCG) method. The preconditioner can be thought of as a generalization of the well-known T. Chan’s preconditioner. For Hermitian positive definite matrix, we observe that our preconditioner is also Hermitian positive definite. The operation cost and convergence of the PCG method are discussed. Numerical experiments have been performed on structured problems to show the competitiveness of this preconditioner.