This paper presents a novel three phase to two phase matrix converter, which performs a direct ac to ac conversion without having a dc link. In opposite to common matrix converters a very high output frequency is demanded for supplying a resonant load (contactless energy transmission system). This gives additional challenges, especially for the switch commutation and the hardware prototyping. Based upon a basic description of the converter, the build prototype and measurements are presented. While the main benefit of the derived commutation strategy - the minimization of commutation steps and independence from the sign of the load current - could be proved, several parasitic elements influence the commutation and lead to an unexpected soft-turn off of the semiconductors. Detailed investigations make the individual parasitics and their special influence visible.