Few switching transitions in high power and medium voltage application of Power converters are desirable. The selective harmonics elimination (SHE) pulse width modulation offers a better quality waveform with lower switching transitions and hence lower switching losses. The SHE is a pre-programmed modulation technique where certain amounts of lower order harmonics are removed and fundamental voltage is controlled. After Fourier analysis of output waveform, a set of nonlinear transcendental equations is obtained which exhibits, multiple, unique or no solution in different range of modulation index (MI). In this paper, an iterative method based on the Jacobian estimate is proposed to solve a highly non-linear set of SHE equations. The proposed technique is easy in implementation and can solve a large number of such equations as computation of the Jacobian matrix in the subsequent iteration is estimated from the previous values. Moreover, the proposed method also removes the singularity problem, especially for large SHE equations. High accuracy in the initial guess is also not essential for this method and can converge to the solution with any random initial guess. The computational and simulation results are given to validate the concept. The hardware result is provided to confirm the computational and simulation results.