  This paper presents a method for expressing the determinant of an N {\times}
N complex block matrix in terms of its constituent blocks. The result allows
one to reduce the determinant of a matrix with N^2 blocks to the product of the
determinants of N distinct combinations of single blocks. This procedure proves
useful in the analytic description of physical systems with multiple discrete
variables, as it provides a systematic method for evaluating determinants which
might otherwise be analytically intractable.
