This paper presents a new switching strategy controling the most-common, simple, and well-known three-phase six-switch voltage source inverter (VSI). Via this strategy, each one of the six transistors conducts for 150°, instead of the known 180° or 120° conduction-modes, resulting in a new space voltage-vector diagram (SVD). For a wye-load connected to the VSI, the known 6 active and 2 zero voltage-vectors, coincided in the origin, construct the classical 7-SVD. Using the new controling strategy, new different 6 non-zero voltage-vectors are primarily introduced to the literature and added to the former ones conistituting an innovated 13 space vector diagram (13-SVD) for the inverter, instead of the conventional 7-SVD. The output phase-voltage becomes a 7-level, 12-step waveform, and a 50% reduction of the total harmonic distortion is obtained. Comprehensive study for the new switching strategy and the resulting voltage vectors is proposed, and comparisons with other VSI topologies; like neutral point clamped (NPC) and multilevel inverters (MLI) were also carried out. Simulation and experimental results show the contribution of the proposed technique.