  For the first time the antineutrino spectrum formed as a result of neutron
and tritium decays during the epoch of primordial nucleosynthesis is
calculated. This spectrum is a non-thermal increase in addition to the standard
cosmic neutrino background (C$\nu$B) whose thermal spectrum was formed before
the beginning of primordial nucleosynthesis. For energy larger than
$10^{-2}\,$eV the calculated non-thermal antineutrino flux exceeds the C$\nu$B
spectrum and there are no other comparable sources of antineutrino in this
range. The observations of these antineutrinos will allow us to look directly
at the very early Universe and non-equilibrium processes taken place before,
during, and some time after primordial nucleosynthesis.
