  The first-generation stars in the $\Lambda$CDM universe are considered to
have formed in dark halos with total masses in the range $\sim
10^{5}-10^{7}M_sun$ at $z \sim 20-50$. These stars expected to be very massive
and in some cases they end their lives as the first supernovae (SNe). We
explore the problem of whether star formation in low mass dark halos (< 10^{7}
M_sun) was triggered or suppressed by the SN feedback from neighboring
star-forming halos. We take into consideration mainly two effects by the SN
shock: one is the evacuation of gas components from the halos and the other is
the promotion of H_2 formation because of the enhanced ionization degree by
shock heating. Combining above effects, we find that the star formation
activities in the neighboring dark matter halos (M < 10^{7} M_sun) are
basically suppressed in case they are located close to the SN center, because
of the gas evacuation effect. The critical distance within which the gas is
blown away falls within the range $\sim 0.3-1.5$kpc depending on the SN energy
and the halo mass. In addition, we find there is very little window in the
parameter space where star formation activities in dark halos are induced or
promoted by neighboring SN.
