In this paper, we propose a new method to extract the singular part fr
om the linear metric perturbation induced by a point particle moving o
n a Schwarzschild/Kerr black hole. The only assumption we make is a ki
nd of analiticity of the resulting metric perturbation around the part
icle. The method is expected to be useful in investigating the gravita
tional radiation reaction to the motion of the particle, its spin, and
so on.