  The retarded Green function for linear field perturbations of black hole
spacetimes is notoriously difficult to calculate. One of the difficulties is
due to a Dirac-$\delta$ divergence that the Green function possesses when the
two spacetime points are connected by a "direct" null geodesic. We present a
procedure which notably aids its calculation in the case of Schwarzschild
spacetime by separating this direct $\delta$-divergence from the remainder of
the retarded Green function. More precisely, the method consists of calculating
the multipolar $\ell$-modes of the direct $\delta$-divergence and subtracting
them from the corresponding modes of the retarded Green function. We illustrate
the usefulness of the method with some specific calculations in the case of the
scalar Green function and self-field for a point scalar charge in Schwarzschild
spacetime.
