Summary We present an efficient variant of the Hermitian and skew‐Hermitian splitting (HSS) preconditioner for generalized saddle point problems. By switching the positions of the two splitting matrices in the HSS preconditioner, together with some modifications combined with the relaxation preconditioning technique, we show that the new preconditioner is much closer to the coefficient matrix and easier to be implemented. Theoretical analyses show that the corresponding iteration method converges to the unique solution of the generalized saddle point problem under certain conditions. The spectral properties, including bounds on the eigenvalues and condition numbers of the eigenvectors, for the preconditioned matrix, are also discussed. Finally, numerical experiments are presented to illustrate the effectiveness of the new preconditioner.

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