Reconsideration of the Regge-Wheeler equation

Reconsideration of the Regge-Wheeler equation is processed by using the Painlev'{e} coordinate and “good” timelier to define the initial time. We find that: the Regge-Wheeler equation could has positive imaginary frequency. Because the Regge-Wheeler equation is the odd (angular) perturbation to the Schwarzschild black hole, the conclusion is that the Schwarzschild black hole is unstable with respect to the rotating perturbation.