It has long been claimed that the antisymmetric tensor field of the second rank is longitudinal after quantization. In my opinion, such a situation produces speculations about the violation of the Correspondence Principle. On the basis of the Lagrangian formalism I calculate the Pauli-Lubanski vector of relativistic spin for this field. Even at the classical level it can be equal to zero after applications of well-known constraints. The correct quantization procedure permits us to propose a solution of this puzzle in the modern field theory. Obtained results develop the previous consideration Physica A 214 (1995) 605-618.