We propose a simple structure which provides optimal system-level fault diagnosis. Each unit of a system can diagnose itself using test outcomes generated within its associated structure. This property makes the structure suitable for systems in a distributed environment where no central processor exists for fault diagnosis. We present a simple diagnosis algorithm based on this structure. Furthermore, we show that the proposed structure always exists for every unit in a system whose graph connectiviq is not less than the number of faulty units. We provide some examples of applying this unit-diagnosis approach to such systems as Boolean N-cube, generalized hypercube and DeBrujin networks. Distributed diagnosis can, therefore, be efficiently done for these fault-tolerant systems with results superior to those previously obtained.