  A second order extrapolation method is presented for shell model
calculations, where shell model energies of truncated spaces are well described
as a function of energy variance by quadratic curves and exact shell model
energies can be obtained by the extrapolation. This new extrapolation can give
more precise energy than those of first order extrapolation method. It is also
clarified that first order extrapolation gives a lower limit of shell model
energy. In addition to the energy, we derive the second order extrapolation
formula for expectation values of other observables.
