  We formulate a new method to calculate the gravitational reaction force on a
particle of mass $\mu$ orbiting a massive black hole of mass $M$. In this
formalism, the tail part of the retarded Green function, which is responsible
for the reaction force, is calculated at the level of the Teukolsky equation.
Our method naturally allows a systematic post-Minkowskian (PM) expansion of the
tail part at short distances. As a first step, we consider the case of a
Schwarzschild black hole and explicitly calculate the first post-Newtonian
(1PN) tail part of the Green function. There are, however, a couple of issues
to be resolved before explicitly evaluating the reaction force by applying the
present method. We discuss possible resolutions of these issues.
