  We derive a new recursion relation to obtain the Feynman diagrams of the
Cornwall-Jackiw-Toumboulis(CJT) effective action by using the functional
derivative identities. By using this recursion relation we show the
two-particle-irreducibility of the Feynman diagrams of the CJT effective action
by induction. We apply the recursion relation to obtain the Feynman diagrams of
the CJT effective action up to the four-loop order in case of the bosonic field
theory.
