  The lattice $A_n^*$ is an important lattice because of its covering
properties in low dimensions. Clarkson \cite{Clarkson1999:Anstar} described an
algorithm to compute the nearest lattice point in $A_n^*$ that requires
$O(n\log{n})$ arithmetic operations. In this paper, we describe a new
algorithm. While the complexity is still $O(n\log{n})$, it is significantly
simpler to describe and verify. In practice, we find that the new algorithm
also runs faster.
