This paper studies a linear radial basis function network (RBFN) for unmixing hyperspectral images. The proposed RBFN assumes that the observed pixel reflectances are nonlinear mixtures of known end-members (extracted from a spectral library or estimated with an end-member extraction algorithm), with unknown proportions (usually referred to as abundances). We propose to estimate the model abundances using a linear combination of radial basis functions whose weights are estimated using training samples. The main contribution of this paper is to study an orthogonal least squares algorithm which allows the number of RBFN centers involved in the abundance estimation to be significantly reduced. The resulting abundance estimator is combined with a fully constrained estimation procedure ensuring positivity and sum-to-one constraints for the abundances. The performance of the nonlinear unmixing strategy is evaluated with simulations conducted on synthetic and real data.