In the current source inverters (CSI), which are widely used recently in many applications, in order to reduce the harmonic contents in the output line current, twelve-step waveform is synthesized usually by a phase-shifted addition of the output currents of two single CSI's. In this paper a new method of synthesis of the 12-step current waveform is suggested which employes a main and a new auxiliary inverters having lower capacity, and thus is economically advantageous over the conventional scheme. DC-side commutation and energy rebond circuit as described in Part I are also employed in this proposed twelve-step CIS for effective commutation and high reliability. Experimental results are also given in oscillgrams.