This paper represents new method to determine the optimum switching angles forSelective Harmonic Eliminated PWM (SHEPWM) inverter. Such switching angles aredefined by a set of nonlinear equations to be solved using the Resultant method. This isdone by first converting these equations that specify the harmonic elimination problem intoan equivalent set of polynomial equations. Then, using the mathematical theory ofResultants, all solutions to this equivalent problem can be found without the need for anyinitial guess. The complete solutions for unipolar SHEPWM switching pattern whichproduce the fundamental while not generating specifically chosen harmonics areinvestigated.