The Modular Multilevel Matrix Converter (M3 C), also known as Triple Star Bridge Cells (TSBC) Converter from the family of Modular Multilevel Cascade Converter (MMCC) has taken importance in medium frequency (MF) applications due to its modularity, redundancy, and high power quality. On the other hand, a Nearest Level Control (NLC) strategy for a medium frequency modulation is a good option due to its low/fundamental switching frequency. However, this method requires a limitation in the switching algorithm; since it is an open loop method is possible that the switching times increase unnecessarily in the operation of the system. This paper presents an improved sorting algorithm for keeping the low-frequency switching using a fully decoupled current control along with the double αβγ transformation, which allows an internal balancing current control of the n-cells in an M3C converter.