  We compute the anomalous dimension of the fermion field with N_f flavours in
the fundamental representation of a general Lie colour group in the non-abelian
Thirring model at four loops. The implications on the renormalization of the
two point Green's function through the loss of multiplicative renormalizability
of the model in dimensional regularization due to the appearance of evanescent
four fermi operators are considered at length. We observe the appearance of one
new colour group Casimir, d_F^{abcd} d_F^{abcd}, in the final four loop result
and discuss its consequences for the relation of the Knizhnik-Zamolodchikov
critical exponents in the Wess Zumino Witten Novikov model to the non-abelian
Thirring model. Renormalization scheme changes are also considered to ensure
that the underlying Fierz symmetry broken by dimensional regularization is
restored.
