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A novel technique for an efficient and rigorous solution of EM scattering and radiation problems from electrically large objects and large arrays is introduced in this paper. Higher order basis functions are used in the characteristic basis function method (CBFM) to model the source and the geometries. The characteristic basis functions are high level basis functions that are constructed by using the piecewise subdomain higher order basis functions, which leads to a much smaller matrix. This method reduces the requirement of the memory and CPU time and can be used to analysis of large antennas and scatters. Numerical results validate the accuracy of this method.