This study presents a space vector pulsewidth modulation algorithm for five-phase converters operating in the overmodulation region that forbids the use of zero vectors, covering the whole overmodulation range and providing minimum <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">x</i> - <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">y</i> voltages. Avoiding zero vectors reduces the content of low-order current harmonics and, at the same time, reduces the common-mode voltage (CMV) by 40%. The method is first implemented using medium and large voltage space vectors, showing good performance in terms of current harmonic content. Then, the algorithm is applied to the case when four large vectors are used, further reducing the peak-to-peak CMV by 80% and still demonstrating a satisfactory performance. Both methods are experimentally compared to existing overmodulation algorithms obtaining better current quality and lower peak-to-peak CMV.