  Ground-state properties are examined for an extended two-channel Kondo model
where the Hilbert space of the localized states is extended to include a
singlet state in addition to the doublet states. By means of zero-th order
variational wavefunctions with different symmetries, which are associated with
the non-Fermi-liquid and the Fermi-liquid ground states, we demonstrate that
the channel exchange coupling via the localized singlet state stabilizes the
Fermi-liquid wavefunction. The ground-state phase diagrams, which are in
qualitative agreement with the previous study performed by Koga and Shiba, are
obtained. The comparison to the structure of the resultant wavefunctions
suggests that a unique non-Fermi-liquid (Fermi-liquid) fixed point exists,
irrespective of the localized ground state.
