  Let $(M,g)$ be a noncompact complete Bach-flat manifold with positive Yamabe
constant. We prove that $(M,g)$ is flat if $(M, g)$ has zero scalar curvature
and sufficiently small $L_{2}$ bound of curvature tensor. When $(M, g)$ has
nonconstant scalar curvature, we prove that $(M, g)$ is conformal to the flat
space if $(M, g)$ has sufficiently small $L_2$ bound of curvature tensor and
$L_{4/3}$ bound of scalar curvature.
