Subsonic bypass turbojet engines of the fifth generation have reached technical maturity, with overall efficiency of 35–38%. Without changing the thermodynamic cycle of the engine, any further work in this direction is futile. The researcher proposes a method of increasing the thermodynamic effectiveness of heat engines based on the so called internal thermodynamic cycles (Pismennyi cycles). The internal cycles possess remarkable characteristics: they increase the effective work output and the heat engine efficiency (thermal and effective); furthermore, they remove temperature restrictions. A gas dynamic design of a bypass turbojet engine is developed based on the internal thermodynamic cycle. Two heat exchangers (circulating and regenerating) are installed in the bypass duct, the first of which can increase the gas temperature before the fan to 2300 K and higher, while the second one can cool the exhaust temperature down to the level comparable to the air temperature behind the fan. Depending on the thrust, general efficiency of the engine in cruise mode (H = 11 km, M = 0.8) can reach 45–55 %. Compared to bypass turbojet engines of the fifth generation (Trent 1000, GP7270, PW4460, etc.), fuel savings with the new design are estimated to be more than 20 %. With the adoption of the proposed jet engine design the total economic impact for airlines can exceed $10 billion annually.