To reduce the computational complexity of classification systems using tangent distance, Hastie et al. rithm to devise rich models for representing large subsets of the data which computes automatically the "best" associated tan(cid:173) gent subspace. We propose a gradient based constructive learning algorithm for building a tangent subspace model with discriminant capabilities which combines several of the the advantages of both HSS and Diabolo: devised tangent models hold discriminant capabilities, space requirements are improved with respect to HSS since our algorithm is discriminant and thus it needs fewer prototype models, dimension of the tangent subspace is determined automatically by the constructive algorithm, and our algorithm is able to learn new transformations.