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A new method to improve the accuracy and efficiency of characteristic mode (CM) decomposition for perfectly conducting bodies is presented. The method uses the expansion of the Green dyadic in spherical vector waves. This expansion is utilized in the method-of-moment (MoM) solution of the electric-field integral equation to factorize the real part of the impedance matrix. The factorization is then employed in the computation of CMs, which improves the accuracy as well as the computational speed. An additional benefit is a rapid computation of far fields. The method can easily be integrated into existing MoM solvers. Several structures are investigated, illustrating the improved accuracy and performance of the new method.