  We investigated the evolution of the black hole binary formed by the merging
of two galaxies each containing a central massive black hole. Our main goal
here is to determine if the black hole binary can merge through the hardening
by dynamical friction and the gravitational wave radiation. We performed
$N$-body simulations of merging of two galaxies with wide range of total number
of particles to investigate the effect of the number of particles on the
evolution of the black hole binary. We found that the evolution timescale was
independent of the number of particles in the galaxy $N$ until the separation
reaches a critical value. After the separation became smaller than this
critical value, the evolution timescale was longer for larger number of
particles. Qualitatively, this behavior is understood naturally the result the
``loss-cone'' effect. However, the dependence of the timescale on $N$ is
noticeably weaker than the theoretical prediction. In addition, the critical
separation is smaller than the theoretical prediction. The timescale of
evolution through gravitational radiation at this critical separation is longer
than the Hubble time. We discuss the reason of these discrepancy and the
implication of the present result on the structure of the ellipticals and QSO
activities.
