A computational method for obtaining the reduced energy values of rigid asymmetric top molecules has been developed for the Mercury computer of the Computing Center of the University of Buenos Aires. The precision achieved is in agreement with the experimental development of microwave spectroscopy. The elements of the tridiagonal submatrices E+, E−, O+, O− have been written in terms of the asymmetry parameter b. The eigenvalues of the matrices are found by solving the characteristic polynomials by an iterative method in the following was: a rough approximation is obtained using a library program, and then the calculations are refined using regula falsi and dichotomous methods in double-length arithmetic. The reduced energy levels are calculated to eight significant figures, even on values corresponding to large quantum rotational numbers J. The method has been tried up to J = 25 with satisfactory results.