  We examine the anisotropy of a four-point correlation function
$G_4(\vec{k},\vec{r};t)$ and it's associated structure factor
$S_4(\vec{k},\vec{q};t)$ calculated using Brownian Dynamics computer
simulations of a model glass forming system. These correlation functions
measure the spatial correlations of the relaxation of different particles, and
we examine the time and temperature dependence of the anisotropy. We find that
the anisotropy is strongest at nearest neighbor distances at time scales
corresponding to the peak of the non-Gaussian parameter $\alpha_2(t) = 3 <
\delta r^4(t) >/[ 5 < \delta r^2(t) >^2] - 1$, but is still pronounced around
the $\alpha$ relaxation time. We find that the structure factor
$S_4(\vec{k},\vec{q};t)$ is anisotropic even for the smallest wave vector
accessible in our simulation suggesting that our system (and other systems
commonly used in computer simulations) may be too small to extract the $\vec{q}
\to 0$ limit of the structure factor. We find that the determination of a
dynamic correlation length from $S_4(\vec{k},\vec{q};t)$ is influenced by the
anisotropy. We extract an effective anisotropic dynamic correlation length from
the small $q$ behavior of $S_4(\vec{k},\vec{q};t)$.
