  We prove that a $4-$dimensional $C^2$ conformally compact Einstein manifold
with H\"older continuous scalar curvature and with $C^{m,\alpha}$ boundary
metric has a $C^{m,\alpha}$ compactification. We also study the regularity of
the new structure and the new defining function. This is a supplementary proof
of Anderson's work and an improvement of Helliwell's result in dimension 4.
