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In this talk,we study a splitting method for an important class of symmetric and indefinite systems.Theoretical analyses show that this method converges to the unique solution of the system of linear equations for all t>0(t is the parameter).Moreover,all the eigenvalue s of the iteration matrix are real and nonnegative and the spectral radius of the iteration matrix is decreasing with respect to the parameter t.Besides,a preconditioning strategy based on the splitting of the symmetric and indefinite coefficient matrices is proposed.The eigensolution of the preconditioned matrix is described and an upper bound of the degree of the minimal polynomials for the preconditioned matrix is obtained.Finally,some numerical experiments are presented to illustrate the effectiveness of the proposed splitting preconditioner.