Lagrange Anchor and Characteristic Symmetries of Free Massless Fields

A Poincar\'e covariant Lagrange anchor is found for the non-Lagrangian relativistic wave equations of Bargmann and Wigner describing free massless fields of spin $s>1/2$ in four-dimensional Minkowski space. By making use of this Lagrange anchor, we assign a symmetry to each conservation law and perform the path-integral quantization of the theory.