  This note provides a conditional Berry-Esseen bound for the sum of a
martingale difference sequence $\{X_i\}_{i=1}^n$ in $\mathbb{R}^d$, $d\ge 1$,
adapted to a filtration $\{\mathcal{F}_i\}_{i=1}^n$. We approximate the
conditional distribution of $S=\sum_{i=1}^n X_i$ given some $\sigma$-field
$\mathcal{F}_0\subset \mathcal{F}_1$ by that of a mean-zero normal random
vector having the same conditional variance given $\mathcal{F}_0 $ as the
vector $S$. Assuming that the conditional variances
$\mathsf{E}[X_iX_i^{\top}\mid\mathcal{F}_{i-1}]$, $i\ge 1$, are
$\mathcal{F}_0$-measurable and non-singular, and the third conditional moments
of $\|X_i\|$, $ i\ge 1 $, given $\mathcal{F}_0$ are uniformly bounded, we
present a simple bound on the conditional Kolmogorov distance between $S$ and
its approximation given $\mathcal{F}_0$ which is of order
$O_{a.s.}([\ln(ed)]^{5/4}n^{-1/4})$.
