  We give a mean-field calculation for the odd-resonating-valence-bond ORVB
pairing scheme. We obtain interesting quasi-particle excitation energy $E_{\bf
k}$ as a function of momentum ${\bf k}$. It is distinctively different from
those of the $d_{x^2-y^2}$-wave, the anisotropic-s-wave, and the p-wave. It is
a gapless theory for superconductivity with well defined Fermi surface. The
ground state of the ORVB scheme is not an eigenstate of the parity or the
time-reversal transformation, thus both symmetries are violated. Some of them
are already manifested in $E_{\bf k}\neq E_{-{\bf k}} $. It is interesting to
find out if such pairing order-parameter scheme exits in some materials in
nature.
