  It is still unknown how the BBH evolves after its semi-major axis reached to
the sub-parsec/parsec scale where the dynamical friction with the neighboring
stars is no longer effective (the so-called the final parsec problem). In this
paper, we propose a new mechanism by which the massive BBH can naturally
coalesce within a Hubble time. We study the evolution of the BBH with triple
disks which are composed of an accretion disk around each black hole and one
circumbinary disk surrounding them. While the circumbinary disk removes the
orbital angular momentum of the BBH via the binary-disk resonant interaction,
the mass transfer from the circumbinary disk to each black hole adds some
fraction of its angular momentum to the orbital angular momentum of the BBH. We
find that there is a critical value of the mass-transfer rate where the
extraction of the orbital angular momentum from the BBH is balanced with the
addition of the orbital angular momentum to the BBH. The semi-major axis of the
BBH decays with time whereas the orbital eccentricity of the BBH grows with
time, if the mass transfer rate is smaller than the critical one, and vice
versa. Its evolutionary timescale is characterized by the product of the
viscous timescale of the circumbinary disk and the ratio of the total black
hole mass to the mass of the circumbinary disk. Since a minimum value of the
critical mass-transfer rate is larger than the Eddington accretion rate of
massive black holes with masses in the 10^{6}M_{sun} to $10^{9}M_{sun} range,
it is promising that the critical mass-transfer rate is larger than the mass
transfer rate. Most of massive BBHs, therefore, enable to merge within a Hubble
time by the proposed mechanism, which helps to solve the final parsec problem.
