The problem of evaluating the stability bounds of discrete-time singularly perturbed systems is considered. A direct method using critical stability criteria has been developed to obtain the exact upper bound epsilon(0) of the singular perturbation parameter epsilon for which the overall system will remain stable For All epsilon is an element of [0, epsilon(0)) The concept of the block bialternate product is utilised to substantially reduce the order of the matrices to be dealt with. It appears that the proposed method is more efficient than that suggested by Li and Li (1992), which makes use of the generalised Nyquist plot. It also completely removes the computational complexity associated with the quadratic dependence on the system matrix A(epsilon) as encountered by Tesi and Vicino (1990).