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This paper applies the selective harmonic elimination (SHE) technique to determine the switching angles for a multilevel inverter that cooperated with specially connected transformer, zig-zag connection. With the ability to direct controlling harmonics, SHE technique has the adaptability to associate with apparatus which are congenitally immune to specific harmonics, such as the zig-zag connection transformers. In this paper the two sets of primary windings of the transformers are supplied by two 6-switch full-bridge inverters with 30 electrical degrees phase shift. Prohibited by the transformers, harmonics with orders other than 12nÂ±1 (n is positive integral) will not appear in the line-to-line voltage of the secondary side. Then, SHE technique is employed to handle harmonics with orders equal to 12nÂ±1, and controls the amplitude of the fundamental. This paper obtains a set of precise switching angles through off-line calculation and then employs a digital signal processor to implement on-line calculation of the switching angles by an approximate method. Some selected analysis and experimental results are shown in this paper. A small-size prototype is built to verify the validity of the proposed system.