Intentional frequency mistuning referred to as detuning is known to be an effective mean to prevent aeroelastic flutter in gas turbines. The Coriolis effect, which is usually discarded, can reduce the mistuning effects and therefore compromise the stabilizing effect of detuning with respect to flutter. This paper presents an original study of the influence of the Coriolis effect on the aeroelastic stability of a single-piece bladed disk (blisk), which made it possible to highlight for the first time the complex interactions between flutter, mistuning, and the Coriolis effect. The blisk is modeled with a lumped parameter model and the aeroelastic self-excitations using Whitehead's theory. A genetic algorithm is used to determine the best detuning pattern to stabilize the flutter-prone blisk. The results show that if the detuning pattern is identified without taking the Coriolis effect into account, the detuned blisk can still be prone to flutter. The key driver of this loss of stability is the frequency separation of the modes resulting from the Coriolis effect, which decreases the mode interactions that are required to stabilize the system. This article demonstrates the need to consider the Coriolis effect when studying the aeroelastic stability of cyclic structures with flexible disk and blade-disk coupling. By doing so, it is shown that a higher level of detuning is needed to compensate the adverse effects of Coriolis and ensure stability to flutter.