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Based on the singularity of electric field integral equation (EFIE), a near-field sparse approximate inverse (SAI) preconditioning technique is proposed to improve the convergence property of the Krylov iterative solution of the dense linear systems arising from EFIE. The multilevel fast multipole algorithm (MLFMA) is employed to reduce the computational complexity of the matrix-vector product operations. Sparse patterns are prescribed by taking account of the interactions of nearby pairs of RWG basis functions. Then, the SAI preconditioner is constructed by Frobenius norm minimization method. It is applied to solve the scattering problem of a PEC plate and a sphere. The additional CPU time and memory consumption are approximately in linear proportion to the number of unknowns. The high numerical efficiency of the proposed preconditioning technique combined with GMRES is illustrated.