  Observations of the inspiral of massive binary black holes (BBH) in the Laser
Interferometer Space Antenna (LISA) and stellar mass binary black holes in the
European Gravitational-Wave Observatory (EGO) offer an unique opportunity to
test the non-linear structure of general relativity. For a binary composed of
two non-spinning black holes, the non-linear general relativistic effects
depend only on the masses of the constituents. In a recent letter, we explored
the possibility of a test to determine all the post-Newtonian coefficients in
the gravitational wave-phasing.
  However, mutual covariances dilute the effectiveness of such a test. In this
paper, we propose a more powerful test in which the various post-Newtonian
coefficients in the gravitational wave phasing are systematically measured by
treating three of them as independent parameters and demanding their mutual
consistency. LISA (EGO) will observe BBH inspirals with a signal-to-noise ratio
of more than 1000 (100) and thereby test the self-consistency of each of the
nine post-Newtonian coefficients that have so-far been computed, by measuring
the lower order coefficients to a relative accuracy of $\sim 10^{-5}$
(respectively, $\sim 10^{-4}$) and the higher order coefficients to a relative
accuracy in the range $10^{-4}$-0.1 (respectively, $10^{-3}$-1).
