  This paper proves that every planar graph $G$ contains a matching $M$ such
that the Alon-Tarsi number of $G-M$ is at most $4$. As a consequence, $G-M$ is
$4$-paintable, and hence $G$ itself is $1$-defective $4$-paintable. This
improves a result of Cushing and Kierstead [Planar Graphs are 1-relaxed,
4-choosable, {\em European Journal of Combinatorics} 31(2010),1385-1397], who
proved that every planar graph is $1$-defective $4$-choosable.
