Abstract: An improved rotary internal combustion engine utilizing a new and improved cycle of operation which includes six phases: intake, compression, combustion, after burn, adiabatic expansion, and exhaust. The purpose of both the after burn phase and the adiabatic expansion phase is to increase the thermodynamic efficiency of the engine and also to reduce the pollution products of the exhaust. The after burn phase achieves this purpose by injecting jets of hot compressed air into the hot combustion phase products at the end of the combustion phase and thus promotes more complete combustion. The adiabatic expansion phase serves to increase the engine efficiency by substantially allowing the combustion products to expand inside the engine thus converting the heat energy into useful mechanical energy.