  We present an alternative scheme for calculating the unrestricted
Hartree-Fock equation. The scheme is based on the variational method utilizing
the sophisticated basis functions that include no adjustable parameters. The
validity and accuracy of the present scheme are confirmed by actual
calculations of the boron and neon atoms. It is shown that the present scheme
not only gives the reasonably lower total energy but also conserves the virial
relation with enough accuracy.
