The recently proposed relation between conformal field theories in two dimensions and supersymmetric gauge theories in four dimensions predicts the existence of the distinguished basis in the space of local fields in CFT. This basis has a number of remarkable properties: one of them is the complete factorization of the coefficients of the operator product expansion. We consider a particular case of the U(r) gauge theory on C2/Zp which corresponds to a certain coset conformal field theory and describe the properties of this basis. We argue that in the case p = 2, r = 2 there exist different bases. We give an explicit construction of one of them. For another basis we propose the formula for matrix elements.
