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Recently, Zhang [Numerical Linear Algebra with Applications, 2018: e2166] constructed an efficient variant of Hermitian and skew-Hermitian splitting (HSS) preconditioner for generalized saddle point problems, and gave the corresponding theoretical analysis and numerical experiment. In this paper, based on the efficient variant of the HSS (EVHSS) preconditioner, we relax the strong condition on the iterative parameter α , generalize the algorithms and further present the modified variant of Hermitian and skew-Hermitian splitting (HSS) (MVHSS) preconditioner for solving the generalized saddle point problem. Moreover, by similar theoretical analysis, we obtain that the MVHSS iterative method is convergent under weaker conditions. Finally, an example is given to verify the effectiveness of the proposed method. MSC : 65F10; 65F15; 65F50