  The attractor mechanism for the four-dimensional ${\cal N}=2$ supergravity
black hole solution is analyzed in the case of the D0-D4 system. Our analyses
are based on newly derived exact solutions, which exhibit explicitly the
attractor mechanism for extremal non-BPS black holes. Our solutions account for
the moduli as general complex fields, while in almost all non-BPS solutions
obtained previously, the moduli fields are restricted to be purely imaginary.
It is also pointed out that our moduli solutions contain an extra parameter
that is not contained in solutions obtained by replacing the charges in the
double extremal moduli solutions by the corresponding harmonic functions.
