Multilevel converters have gained significant popularity in medium-voltage and high-power applications due to their numerous advantages over traditional two-level converters. These advantages include reduced harmonic distortion, improved efficiency, and lower stress on power semiconductors. Selective harmonic elimination (SHE) is a modulation method that can be employed with multilevel converters to achieve high-quality output voltage waveforms. In this work, an extension of Broyden’s method, known as the Quasi-Modified Newton Method, is implemented for selective harmonic elimination and accurate calculation of switching angles for a wide range of modulation indices. The proposed method is applied to cascaded H bridge inverters operating at levels 5, 7, and 9. The method offers simplicity, reduced computational burden, and faster convergence, making it easily implementable, reducing total harmonic distortion (THD), and reducing RMSE and MAD errors. The paper includes simulation and experimental results that validate the accuracy and effectiveness of the proposed approach.