Our paper proposes an implementable procedure for using the method of quasi-random sequences in software debug testing. In random testing, the sequence of tests (if considered as points in an n-dimensional unit hypercube) will give rise to regions where there are clusters of points, as well as underpopulated regions. Quasi-random sequences, also known as low-discrepancy or low-dispersion sequences, are sequences of points in such a hypercube that are spread more evenly throughout. Based on the observation that program faults tend to lead to contiguous failure regions within a program's input domain, and that an even spread of random tests enhances the failure detection effectiveness for certain failure patterns, we examine the use of quasi-random sequences as a replacement for random sequences in automated testing. Because there are only a small number of quasi-random sequence generation algorithms, and each of them can only generate a small number of distinct sequences, the applicability of quasi-random sequences in testing real programs is severely restricted. To alleviate this problem, we examine the use of two types of randomized quasi-random sequences, which are quasi-random sequences permuted in a nondeterministic fashion in such a way as to retain their low discrepancy properties. We show that testing using randomized quasi-random sequences is often significantly more effective than random testing.