  We study a sufficient condition to prove the stability of a black hole when
the master equation for linear perturbation takes the form of the Schr\"odinger
equation. If the potential contains a small negative region, usually, the
$S$-deformation method was used to show the non-existence of unstable mode.
However, in some cases, it is hard to find an appropriate deformation function
analytically because the only way known so far to find it is a try-and-error
approach. In this paper, we show that it is easy to find a regular deformation
function by numerically solving the differential equation such that the
deformed potential vanishes everywhere, when the spacetime is stable. Even if
the spacetime is almost marginally stable, our method still works. We also
discuss a simple toy model which can be solved analytically, and show the
condition for the non-existence of a bound state is the same as that for the
existence of a regular solution for the differential equation in our method.
From these results, we conjecture that our criteria is also a necessary
condition.
