Debugging software often involves a removal process: the process of detection and removal of faults from a program. This paper gives an e4cient procedure to detect all faults in a software item with high probability. The procedure is such that at any step the probability of leaving just one fault is equal to some speci6ed value: the probability of leaving more than one fault is much smaller. It is found that, after eliminating the risk of early stopping, the probability of incomplete detection is then only slightly greater than). The performance of the proposed procedure is demonstrated by simulation and by application to a real example.