Abstract: The eigenvalue estimate theory of saddle point matrices is studied. Estimate for the lower bound of the maximum eigenvalues of saddle point matrices is improved, based on the analysis of the symmetry of saddle point matrices and the relation between maximum eigenvalues of saddle point matrices and the eigenvalues of their sub-matrices. Then, an improved interval estimate for the maximum eigenvalues of saddle point matrices is obtained. The maximum eigenvalues of saddle point matrices, which are derived from the stationary Stokes equation discretized by the P1-P0 mixed finite element method, are observed in the numerical experiment. The numerical results demonstrate that the involved interval estimate for the maximum eigenvalues of saddle point matrices is valid.