  This note is a continuation of the author's paper \cite{Li}. We prove that if
the metric $g$ of a 4-manifold has bounded Ricci curvature and the curvature
has no local concentration everywhere, then it can be smoothed to a metric with
bounded sectional curvature. Here we don't assume the bound for local Sobolev
constant of $g$ and hence this smoothing result can be applied to the
collapsing case.
