Calculating the Fierz Transformation for Higher Orders
  We consider the higher-order Fierz transformation, which corresponds to expanding a product of $\bar\psi\Gamma\psi$ terms into a sum of products of Dirac densities and currents. It is shown that the Fierz transformation can be obtained by solving a large system of linear equations with fractional complex coefficients, which is practical at least up to fourth power. 
J. A. Maruhn, T. Buervenich, D. G. Madland