Abstract The quadrupole and octupole contributions to the gravitational radiation flux at null infinity from an initially stationary isolated system are computed in terms of the asymptotic moments defined there. The present treatment incorporates the influence of the background field of the source while still neglecting the nonlinear self-interaction of the radiation. Compared with the flat space result, the new formula predicts a suppression of the contribution from the high-frequency modes for which the frequency ω satisfies GM0ω/c3 ≫ 1, M0 being the initial mass of the system.