Purpose – This paper proposes an improved algorithm to compute selective harmonics elimination pulse width modulation (SHEPWM) angles, based on the Newton-Raphson (NR) iteration for cascaded multilevel inverter (CMI). Design/methodology/approach – Newton Raphson (NR) is a very popular numerical method for transcendental equations that lack analytical solutions. It has been successfully used to compute the angles for selective harmonics elimination pulse width modulation (SHEPWM) schemes. Despite its effectiveness, NR has not been used for SHEPWM with cascaded multilevel inverter (CMI) structure with equal and non-equal DC voltage sources. It is known that for CMI, inappropriate selection of initial angles causes long-iteration time and possibly non-convergence takes place. The computational difficulty is compounded by the fact that the SHEPWM switching angles need to be correctly sequenced, i.e. each angle must be assigned to the correct output voltage level of the CMI. In this work, an attempt is made to reduce the iteration time and to resolve the non-convergence problem. The main idea is to relax the switching angle constraint by placing the switching angle sequencing outside the main loop of NR iteration. This allows for the program to run more freely and able to generate more possible solutions for the switching angles. Then these angles are selected to fulfill the requirements of multilevel sequencing. The performance of the proposed technique will be compared with the standard NR for CMI with equal and non-equal DC sources. The latter case is quite common for CMI with renewable energy applications because the sources normally have different voltage levels. Findings – Using MATLAB simulation, it will be shown that using this scheme, accurate SHEPWM angles can be achieved for a wide range of fundamental components. Furthermore, significant reduction in iteration time to compute the SHEPWM switching angles is achieved. Originality/value – This paper proposes an improved algorithm to compute SHEPWM angles based on NR iteration. [ABSTRACT FROM AUTHOR]