  Generally, the Schwarzschild black hole was proved stable through two
different methods: the mode-decomposition method and the integral method. In
the paper, we show the integral method can only apply to the initial data
vanishing at both the horizon and the spatial infinity. It can not treat the
initial data only vanishing at the spatial infinity. We give an example to show
the misleading information caused by the use of the tortoise coordinates in the
perturbation equations. Subsequently, the perturbation equation in the
Schwarzschild coordinates is shown not sufficient for the stable study.
