  Let $P$ be a planar set of $n$ points in general position. We consider the
problem of computing an orientation of the plane for which the Rectilinear
Convex Hull of $P$ has minimum area. Bae et al. (Computational Geometry: Theory
and Applications, Vol. 42, 2009) solved the problem in quadratic time and
linear space. We describe an algorithm that reduces this time complexity to
$\Theta(n \log n)$.
