We apply the nested algebraic Bethe ansatz method to solve the eigenvalue p
roblem for the SU(4) extension of the Hubbard model. The Hamiltonian is equ
ivalent to the SU(4) graded permutation operator. The graded Yang-Baxter eq
uation and the graded Quantum Inverse Scattering Method are used to obtain
the eigenvalue of the SU(4) extension of the Hubbard model.