The pion is important in nuclear physics. However, there is a difficulty to treat pion due to its strong tensor interaction. The Hartree-Fock (HF) state for spin-saturated nucleus provides zero matrix element for the tensor operator. Hence, we ought to extend the model space to include 2p-2h states in order for the tensor interaction to have a finite matrix element. The variational principle of the total energy provides equations for the amplitudes of 2p-2h states and also the HF single particle wave functions. The differential equation for HF single particle states resemble the Brueckner-Hartree-Fock (BHF) equation. Hence, we name the new framework as extended Brueckner-Hartree-Fock (EBHF) theory. The EBHF theory shows that there is a defect in the BHF framework. We are now able to solve for finite nuclei in the EBHF theory with bare nucleon-nucleon interaction.