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A new compact 2-D full-wave algorithm based on the Yee's grid, is developed for propagation constant computation. Unlike other 2-D Yee's grid based techniques (which require an initial input parameter of phase constant value in order to extract the resonant domain information), this computes the propagation constant directly from a given frequency. The technique has no stability problems and offers potential fast computation speed and better accuracy over the existing 2D time-domain approaches. Sparse matrix technique is used to minimize the memory requirement and CPU time. Numerical results are presented and are compared to other literatures.