Considering the aim of having low switching losses, especially in medium-voltage and high-power converters, the pre-programmed pulse width modulation technique is very useful because the generated harmonic content can be known in advance and optimized. Among the different low switching frequency techniques, the Selective Harmonics Elimination (SHE) modulation method is most suitable because of its direct control over the harmonic spectrum. This paper proposes a method for obtaining multiple solutions for selectively eliminating specific harmonics in a wide range of modulation indices by using modified Newton–Raphson (NR) and pattern generation techniques. The different pattern generation and synthesis approach provide more degrees of freedom and a way to operate the converter in a wide range of modulation. The modified Newton–Raphson technique is not complex and ensures fast convergence on a solution. Moreover, multiple solutions are obtained by keeping a very small increase in the modulation index. In the previous methods, solutions were not obtainable at all modulation indices. In this paper, only exact solutions to the low-order harmonics elimination for Cascaded H-bridge inverter are reported for all modulation indices. Analytical and simulation results prove the robustness and correctness of the technique proposed in this paper.