  The recent discovery of a hyper metal-poor (HMP) star, whose metallicity Fe/H
is smaller than 1/100,000 of the solar ratio, together with one earlier HMP
star, has raised a challenging question if these HMP stars are the actual first
generation, low mass stars in the Universe. We argue that these HMP stars are
the second generation stars being formed from gases which were chemically
enriched by the first generation supernovae. The key to this solution is the
very unusual abundance patterns of these HMP stars with important similarities
and differences. We can reproduce these abundance features with the
core-collapse ``faint'' supernova models which undergo extensive matter mixing
and fallback during the explosion.
