This paper proposes a selective harmonic elimination technique for medium and high power three phase cascaded H-bridges l-level inverters at fundamental frequency. Compared to other SHE methods, it is capable to delete more harmonics from the output voltage waveform and to provide lower total harmonic distortion values. A mathematical proof is given to demostrate that undeleted harmonics are only those of order n = 2k (l + r) ± 1, k = 1, 2, . . ., where r is an integer parameter that assumes the values −2, −1, 0, de ning three di erent sets of switching angles, provided within the whole range of modulation index. Proposed method assumes the availability of di erent dc voltage sources and pulses patterns, de ned for the three sets of switching angles. Simulated results are shown to con rm the validity of the proposed procedure. For l = 5 and l = 7, obtained results have been compared with those obtained with a conventional SHE technique at the same conditions. Very good performances, in terms of number of deleted harmonics and THD, are observed when r = 0, moreover, in comparison with classical SHE, proposed method o ers reduced computational complexity because it does not require the solution of non linear equations.