  In this paper we derive a refined asymptotic expansion, near an isolated
singularity, for conformally flat metrics with constant positive Q-curvature
and positive scalar curvature. The condition that the metric has constant
Q-curvature forces the conformal factor to satisfy a fourth order nonlinear
partial differential equation with critical Sobolev growth, whose leading term
is the bilaplacian. We model our results on a similar asymptotic expansion for
conformally flat, constant scalar curvature metrics proven by Korevaar, Mazzeo,
Pacard, and Schoen. Along the way we analyze the linearization of the
Q-curvature equation about the Delaunay metrics recently discovered by Frank
and K\"onig, which may be of independent interest.
