If torsion exists, it generates gravitational four-fermion interaction (GFFI), essential on the Planck scale. We analyze the influence of this interaction on the Friedmann-Lemaitre-Robertson-Walker cosmology. An explicit analytic solution is derived for the problem where both the energy-momentum tensor generated by GFFI and the common ultra-relativistic energy-momentum tensor are included. We demonstrate that gravitational four-fermion interaction does not result in a Big Bounce.