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Quasi-random sequences, which can evenly spread points across a hypercube, have been widely used in various areas. Recently, quasi-random testing technique, which makes use of quasi-random sequences to generate test cases, was proposed, and it normally has a higher failure-detection capability than pure random testing. However, there exist only a few distinct quasi-random sequences in the literature, and all these sequences are deterministic rather than random. Therefore, the applicability of quasi-random sequences in testing is restricted. In this paper, we propose a new approach to randomising quasi-random sequences. Out approach can generate many distinct randomised quasi-random sequences that have even distributions of points. The experimental results also show that these sequences can significantly enhance the effectiveness of random testing.