  We show that for $f$ a continuous function on the closed polydisc
$\bar{\mathbb{D}^n}$ with $n\geq 2$, the Hankel operator $H_{f}$ is compact on
the Bergman space of $\mathbb{D}^n$ if and only if there is a decomposition
$f=h+g$, where $h$ is in the ball algebra and $g$ vanishes on the boundary of
the polydisc.
