  Effects of the Dzyaloshinski-Moriya (DM) interaction on low-energy
excitations in a one-dimensional orthogonal-dimer model are studied by using
the perturbation expansions and the numerical diagonalization method. In the
absence of the DM interaction, the triplet excitations show two flat spectra
with three-fold degeneracy, which are labeled by magnetization $M=0,\pm{1}$.
These spectra split into two branches with M=0 and with $M=\pm{1}$ by
switching-on of the DM interaction and besides the curvature appears in the
triplet excitations with $M=\pm 1$ more strongly than those of M=0.
