  We study the evolution of gas in HII regions around the first stars after the
death of the exciting stars. If the first star in a small halo dies without
supernova (SN), subsequent star formation is possible in the same halo. We thus
investigate the effect of ionization of the gas on subsequent star formation
within small halos in the early universe using one-dimensional hydrodynamics
with spherical symmetry along with non-equilibrium primordial gas chemistry. We
find that the enhanced electron fraction facilitates the formation of molecular
hydrogen at the cores of these halos. The low temperature circumstances
produced by the H_2 cooling is suitable for HD formation and the resultant
cooling further drops the temperature below 100 K. Consequently, low-mass stars
with primordial abundances can form even in a small halo. After accreting the
interstellar metals, these stars might resemble low-mass ultra metal-poor stars
discovered in the present Galactic halo.
