Recently there has been an increasing interest in active fault detection when traditional approaches are not effective or cannot be used. Previous papers have shown how to construct continuously varying test (auxiliary) signals for use in fault detection and identification. Such signals may not always be easy to implement. In this paper a new algorithm is presented to compute optimal piecewise constant test signals. In the important case where the test signal changes values a small number of times, the new test signals can be both smaller and more effective than test signals computed by other means. Two computational examples are given to illustrate both computational issues and differences between different types of piecewise constant signals.