In this paper we propose a semi-distributed self-diagnostic algorithm for Hypercube networks which is based on the use of a combinatorial structure known as the Hadamard matrix. We propose a model for providing fault- tolerance to the diagnostic scheme and to analyze the performance of the proposed diagnostic scheme. This analysis provides a tradeoff between the complexity of the algorithm and its level of fault-tolerance. However, the optimal solution to the diagnostic problem with desired level of fault- tolerance is shown to be related to the problem of finding the covering radius of a binary code which is a NP-hard problem for the Hypercube networks. We discuss various cases for n=8, 16, 32. However, for achieving a level of about 50% fault-tolerance for the proposed diagnostic scheme, we provide an optimal solution valid for all Hypercube networks.