  The discrete Fr\'echet distance is a useful similarity measure for comparing
two sequences of points $P=(p_1,\ldots, p_m)$ and $Q=(q_1,\ldots,q_n)$. In many
applications, the quality of the matching can be improved if we let $Q$ undergo
some transformation relative to $P$. In this paper we consider the problem of
finding a translation of $Q$ that brings the discrete Fr\'echet distance
between $P$ and $Q$ to a minimum. We devise an algorithm that computes the
minimum discrete Fr\'echet distance under translation in $\mathbb{R}^2$, and
runs in $O(m^3n^2(1+\log(n/m))\log(m+n))$ time, assuming $m\leq n$. This
improves a previous algorithm of Jiang et al.~\cite{JXZ08}, which runs in
$O(m^3n^3 \log(m + n))$ time.
