Recently there has been growing interest in the technology of high-phase order power transmission, in place of conventional three-phase power transmission, for increasing the power transmission capability of overhead electric power transmission rights-of-way. One of the most important items in applying high-phase order transmission systems (12-phase systems) is the study of the faults that may appear in these systems. This paper starts with a historical review of the Four Three-Phase Symmetrical Components Technique, which was proposed for analyzing the faults that could occur on 12-phase power systems. Then a detailed study of transverse short-circuit faults that could occur on such systems is given in terms of this technique.