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In this paper, interpolatory vector basis functions for a new combined-field surface integral equation (JMCFIE) solved with the method of moments has been presented. This method applied to solve complex electromagnetic scattering problems, like perfect electric conductors, homogeneous dielectric objects, and conductor-dielectric combined structure. New combined-field surface integral equation (JMCFIE) which using Galerkin's method can lead to a well condition MOM matrix, at the same time, higher order basis functions for the expansion of the surface current densities can provide more accurate modeling and reduce the number of unknowns. The multilevel fast multipole algorithm is then employed to reduce the memory requirement and computational complexity.