Thermal efficiency of the ideal Carnot cycle is accepted to be highest of all reversible cycles. Heat is supplied at the highest process of temperature, and rejected at the lowest temperature. The reversible recuperative Joule-Brayton cycle, an ideal gas turbine cycle with heat recuperation, can also reach the Carnot efficiency when the pressure ratio is unity. In the evaporative gas turbine cycle (EGT-cycle), water is injected after the compressor and cools the charged air. More heat can be recuperated, this allows for higher thermal efficiencies. When the reversible recuperative Joule-Brayton cycle reaches the Carnot efficiency for a pressure ratio of unity, and the EGT efficiency is higher, then, it would be possible to top the Carnot cycle efficiency. Here, the authors show that in a... special application of the EGT cycle, the Ostfalia EGT cycle, a higher efficiency than Carnot, can be reached without breaking any thermodynamic laws. In the EGT cycle, the authors can keep the rejected heat constant with increasing heat supply, this leads to a higher effectiveness. The authors can achieve this by increasing the air humidity through water injection, and enlarging the heat recuperation. In the Ostfalia EGT cycle, a very low compression ratio and air saturation is applied. The authors can prove that the isobaric heat rejection takes place beneath the ambient temperature. The amount of heat rejection is the summation of the negative condensation heat of vapor and the positive sensible heat. The Ostfalia EGT cycle remains a thought experiment, its efficiency can only be achieved under ideal and reversible operating conditions.