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Orthogonal search techniques are often used in training generalized single-layer networks (GSLNs) such as the radial basis function (RBF) network. Care must be taken with these techniques in order to avoid ill conditioning of the required data matrix. The usual approach is to impose an arbitrary lower limit, say dmin, on the norms of the orthogonal expansion terms, or equivalently on the diagonal values in the Cholesky decomposition matrices, which are calculated by the algorithms in question. In this paper, a bound on the condition number of the data matrix in terms of these quantities is given, and is used to derive a model-dependent guideline for dmin.