  In this work, we provide a $(n/m)^{-1/2}$-rate finite sample Berry-Esseen
bound for $m$-dependent high-dimensional random vectors over the class of
hyper-rectangles. This bound imposes minimal assumptions on the random vectors
such as nondegenerate covariances and finite third moments. The proof uses
inductive relationships between anti-concentration inequalities and
Berry--Esseen bounds, which are inspired by the telescoping method of Chen and
Shao (2004) and the recursion method of Kuchibhotla and Rinaldo (2020).
Performing a dual induction based on the relationships, we obtain tight
Berry-Esseen bounds for dependent samples.
