In order to include hole motins in the Brueckner method a systematic theory is developed based on a familiar treatment of small oscillations of some dynamical system about the stable point. It is shown that a slight modification in the Bethe-Goldstone equation enables us to take into account all effects coming from the couplings of particle-particle and hole-hole pairs with the same total momentum. Ground state energy is expressed with the sum of zero point energy shifts of all hole pair oscillators. Superfluidity condition found by Bogoliubov, Tolmachev and Shirkov and by Cooper, Mills and Sessler is also derived here as the condition for the stability of the degenerate Fermi gas state. Expression of ground state vector is given. A remark is added on the interpretation of the perturbation expansion.