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Cascaded H-bridge (CHB) multilevel inverter is one of the popular converter topologies for use in high power drives. It is composed of multiple units of single-phase H-bridge inverter power cells. The H-bridge cells are normally connected in cascade on their ac side to achieve high voltage operation and low harmonic distortion. The staircase modulation scheme applied to the CHB inverter is simple to implement since all the switching angles can be calculated off-line and then stored in a look-up table for digital implementation. However, the solving of nonlinear equations for the staircase modulation with selective harmonic elimination (SHE) remains a challenging problem. This paper presents a novel homotopy algorithm which can be effectively used to solve the problem. The proposed algorithm is analyzed in detail, and the solutions of dual bands (Pattern A and B) are provided. The simulation and experimental results are given for verification.