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The preconditioner for parameterized inexact Uzawa methods have been used to solve some indefinite saddle point problems.Firstly,we modify the preconditioner by making it more generalized,then we use theoretical analyses to show that the iteration method converges under certain conditions.Moreover,we discuss the optimal parameter and matrices based on these conditions.Finally,we propose two improved methods.Numerical experiments are provided to show the effectiveness of the modified preconditioner.All methods have fantastic convergence rates by choosing the optimal parameter and matrices.