Summary: We consider here two basic fault-secure scheduling problems for multiprocessor systems. First, given the number of processors in the system and a set of computational tasks of unit length expressed as a complete binary tree, a scheduling algorithm is proposed such that the total execution time is a minimum and no undetected single error result will be delivered. Second, given a deadline and a computation tree, another algorithm is given which generates a fault-secure scheduling using a minimum number of processors. We show that two previous approaches are special cases of these algorithms. We also discuss the way to modify our scheduling to ensure a given fault latency requirement. Finally, extensions that cover multiple errors, non-unit length tasks and computation graphs of arbitrary binary trees are discussed.