  Starting from the Dyson-Beliaev and generalized Gross-Pitaevskii equations
with an extra nonlocal potential, we derive an exact expression of the
two-particle Green's function K for an interacting Bose-Einstein condensate in
terms of unambiguously defined self-energies and vertices. The formula can be a
convenient basis for approximate calculations of K. It also tells us that poles
of K are not shared with (i.e. shifted from) those of the single-particle
Green's function, contrary to the conclusion of previous studies.
