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We discuss the ground state of a two dimensional electron-lattice systemdescribed by a Su-Schrieffer-Heeger type Hamiltonian with a half-filledelectronic 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 patternis not unique in spite of a unique electronic energy spectrum and the sametotal energy. The necessary and sufficient conditions to be satisfied by thedistortion patterns in the ground state are derived numerically. As a resultthe 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.Comment: 2pages, 2figure

Degeneracy of Ground State in Two-Dimensional Electron-Lattice System