A report is presented on the first low-loss monolithic microwave integrated circuit switch using AlInN/GaN heterostructure field effect transistors. Owing to significantly lower sheet resistance compared to the conventional AlGaN/GaN heterostructure (215 against 280 Q/□), and lower contact resistance (0.27 against 0.5 Ω×mm), the microwave switch based on AlInN/GaN shows lower insertion loss (0.8 against 0.9 dB at 6 GHz) and higher isolation (40 against 35 dB at 6 GHz). The achieved performance compares favourably or exceeds published results for this frequency range; even better performance can be achieved considering ultimate parameters for AlInN/GaN heterostructures.