  It has been shown in the author's companion paper that solutions of
Maxwell-Klein-Gordon equations in $\mathbb{R}^{3+1}$ possess some form of
global strong decay properties with data bounded in some weighted energy space.
In this paper, we prove pointwise decay estimates for the solutions for the
case when the initial data are merely small on the scalar field but can be
arbitrarily large on the Maxwell field. This extends the previous result of
Lindblad-Sterbenz \cite{LindbladMKG}, in which smallness was assumed both for
the scalar field and the Maxwell field.
