  In this paper, we look how to construct in Minkowski space-time a new type of
\textit{chiralspin} group transformation of the spinor fields, similar to the
one discovered by recent works of \textit{Glozman et al.} in the context of
high temperature QCD and truncated studies in lattice calculations. Afterwards,
we prove the invariance of free massless fermionic action under such group
transformations, as well the invariance of the Hamiltonian of free massless
fermions. At the end, the possible presence of a symmetry driven by such new
\textit{chiralspin} group at high temperature QCD, also at non zero chemical
potential, is discussed.
