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An improvement of the Airy's function version of the transfer-matrix method for resonant tunneling eliminates numerical problems in low-applied voltages and inefficiency to calculate the energies of quasi-bound states. The method is based on the exact solution of Schrodinger's equation and is useful in checking other computational techniques used in the theory of resonant tunneling. The transmission coefficient, I-V characteristics of finite superlattices, and energies of the bound and quasi-bound states calculated by different methods agree well.