A description of scalar waves scattered off a Schwarzschild black hole
is discussed in terms of complex angular momenta. In the new picture
the scattering amplitude is split into a supposedly smooth background
integral and a sum over the so-called Regge poles. It is proved that a
ll the relevant Regge poles (the singularities of the S-matrix) must b
e situated in the first quadrant of the complex lambda(= l + 1/2)-plan
e. We also show that the S-matrix possesses a global symmetry relation
S(-lambda) = e-2ipi(lambda)S(lambda), which makes it possible to simp
lify considerably the background integral. Finally, a formal basis for
actual computations of Regge poles and the associated residues is out
lined.