If I have a $n\times n$ unimodular matrix $A \in \text{GL}(n,\mathbb Z)$, i.e., with elements $A_{ij} \in \mathbb Z$, is there some way to decompose the matrix into a product of matrices $A=A^{(1)}A^{(2)} \dots A^{(k)}$ such that each $A^{(l)}$ has elements $(A^{(l)}_{ij}-d/2 )\mod d= A^{(l)}_{ij}$, whereby $d$ is an even integer.
For example, if the matrix $A$ is an $n\times n$ matrix with elements such that $\max_{i,j} A_{ij}\le K$ and $\min_{i,j} A_{ij}\ge -K$, we could write $A$ in terms of $k$ matrices whereby each matrix $A^{(l)}$ has elements with values $\max_{i,j} A^{(l)}_{ij}\le d/2$ and $\min_{i,j} A^{(l)}_{ij}\ge -d/2$.