A novel approach to the diagnosis of hypercubes, called Self-Validating Diagnosis, is introduced. An Algorithm based on this approach, called SVD algorithm, is presented and evaluated. Given any fault set and the resulting syndrome, the algorithm returns a diagnosis and a syndrome-dependent bound, Ts, with the property that diagnosis is correct (although possibly incomplete) if the actual number of faulty units is less than Ts. The average of Ts is very large and the diagnosis is almost complete even when the percentage of faulty units in the system approaches 50%. Moreover, the diagnosis correctness can be validated deterministically by individually probing a very small number of units. These results suggest that the SVD algorithm is suitable for applications requiring a large degree of diagnosability as it is the case of wafer-scale testing of VLSI chips, where the percentage of faulty units may be as large as 50%.