  Let $P$ be a set of $n$ points in general position on the plane. A set of
closed convex polygons with vertices in $P$, and with pairwise disjoint
interiors is called a convex decomposition of $P$ if their union is the convex
hull of $P$, and no point of $P$ lies in the interior of the polygons. We show
that there is a convex decomposition of $P$ with at most
$\frac{4}{3}|I(P)|+\frac{1}{3}|B(P)|+1\le \frac{4}{3}|P|-2$ elements, where
$B(P)\subseteq P$ is the set of points at the vertices of the convex hull of
$P$, and $I(P)=P-B(P)$.
