  This work argues that the off-diagonal long range order (ODLRO) is not
necessary for showing superconductivity while the electron pairing around Fermi
surface is sufficient for superconductivity. It is shown that there exists the
pseudogap state associated with the electron pairing in real space and the high
temperature superconductivity could be only found in the metallic region near
the Mott metal insulator transition (MIT).
