  We take into account the dynamics of a complete third post-Newtonian
conservative Hamiltonian of two spinning black holes, where the orbital part
arrives at the third post-Newtonian precision level and the spin-spin part with
the spin-orbit part includes the leading-order and next-to-leading-order
contributions. It is shown through numerical simulations that the
next-to-leading order spin-spin couplings play an important role in chaos. A
dynamical sensitivity to the variation of single parameter is also
investigated. In particular, there are a number of \textit{observable} orbits
whose initial radii are large enough and which become chaotic before
coalescence.
