  In this paper we analyze the invariance of the Dirac equation under disformal
transformations depending on the propagating spinor field. Using the
Weyl-Cartan formalism, we construct a large class of disformal maps between
different metric tensors, respecting the order of differentiability of the
Dirac operator and satisfying the Clifford algebra in both metrics. Then, we
have shown that there is a subclass of solutions of the Dirac equation,
provided by Inomata's condition, which keeps the Dirac operator invariant under
the action of the disformal group.
