  We have examined a Hubbard model on a chain of squares, which was proposed by
Yajima et al as a model of an atomic quantum wire As/Si(100), to show that the
flat-band ferromagnetism according to a kind of Mielke-Tasaki mechanism should
be realized for an appropriate band filling in such a non-frustrated lattice.
Reflecting the fact that the flat band is not a bottom one, the ferromagnetism
vanishes, rather than intensified, as the Hubbard U is increased. The exact
diagonalization method is used to show that the critical value of U is in a
realistic range. We also discussed the robustness of the magnetism against the
degradation of the flatness of the band.
