Summary: Let \(\mathsf{M}(n)\) denote the bit complexity of multiplying \(n\)-bit integers, let \(\omega \in(2, 3]\) be an exponent for matrix multiplication, and let \(\lg^\ast n\) be the iterated logarithm. Assuming that \(\log d = O(n)\) and that \(\mathsf{M}(n) /(n \log n)\) is increasing, we prove that \(d \times d\) matrices with \(n\)-bit integer entries may be multiplied in \[ O(d^2 \mathsf{M}(n) + d^\omega n 2^{O(\lg^\ast n - \lg^\ast d)} \mathsf{M}(\lg d) / \lg d) \] bit operations. In particular, if \(n\) is large compared to \(d\), say \(d = O(\log n)\), then the complexity is only \(O(d^2 \mathsf{M}(n))\).