Non-distinguishability of non-orthogonal quantum states is the essential feature of quantum mechanics. In particular, one cannot deterministically orthogonalize the set of quantum states, while probabilistic orthogonalization is possible, including unambiguous state discrimination and discrimination between the subsets. Here, we propose a method for error-free subsets discrimination with significantly increased success probability, which may reach one even for non-orthogonal and linearly dependent input states. This method may be applied in quantum cryptography: An alternative basis reconciliation procedure is described, which may provide unit sifting probability even for a large number of bases and for non-orthogonal states within each basis.