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In this paper, we describe a new and efficient strategy for solving linear system of equations arising in the application of method of moments to electromagnetic problems. This new approach is based on the use of characteristic basis functions (CBFs) that are defined on macro domains (blocks), and include a relatively large number of conventional sub-domains functions, defined on triangular or rectangular patches. The use CBFs leads to a significant reduction in the number of unknowns, and, as a result, the technique enables us to use a direct solver, as opposed to iteration. Numerical results are presented to demonstrate the accuracy and efficiency of the CBFM when used to solve several test problems.