  We discuss the ground state of a two dimensional electron-lattice system
described by a Su-Schrieffer-Heeger type Hamiltonian with a half-filled
electronic band, for which it has been pointed out in the previous paper [J.
Phys. Soc. Jpn. 69 (2000) 1769-1776] that the ground state distortion pattern
is not unique in spite of a unique electronic energy spectrum and the same
total energy. The necessary and sufficient conditions to be satisfied by the
distortion patterns in the ground state are derived numerically. As a result
the degrees of degeneracy in the ground state is estimated to be about
$N^{N/4}$ for $N \gg 1$ with $N$ the linear dimension of the system.
