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The finite element or finite difference techniques are well known for the solution of Maxwell's equation in the differential form. But terminating the mesh accurately at a finite distance from the body in the case of an open problem is a major challenge. The method of Sadiku (see Numerical Techniques in Electromagnetics, CRC Press, Inc., Boca Raton, 1992) is applied for only the electrostatic problem. This hybrid method is applied for the TM scattering problem and the results are documented in this paper. This new approach, as in the electrostatic case, allows for the terminating surface to encapsulate the body very tightly. As before, the finite element technique is used for open region problems whereas the integral equation solution approach using Green's function is applied to enforce the radiation condition. At each iteration cycle, the induced currents on the conducting cylinder are evaluated and their scattered field at the terminating surface is calculated. Using this method for the TM case, the computational efficiency of the finite element method can be increased. It can be generalized for the case of inhomogeneous and nonlinear media, for static and dynamic fields. Numerical results are presented for the solution of Helmholtz's equation to illustrate the accuracy of the technique.