  It has long been claimed that antisymmetric tensor field of the second rank
is longitudinal after quantization. Such a situation is quite unacceptable from
a viewpoint of the Correspondence Principle. On the basis of the Lagrangian
formalism we calculate the Pauli-Lyuban'sky vector of relativistic spin for
this field. Even at the classical level it can be equal to zero after
application of the well-known constraints. The correct quantization procedure
permits us to propose solution of this puzzle in the modern field theory.
Obtained results develop the previous consideration of Evans [{\it Physica
A}214 (1995) 605-618].
