  We computed the orbital evolution and the emitted gravitational radiation of
the supermassive black hole binary OJ 287. Here we used the initial data
provided by the outburst structure of the system. We considered the spin-spin,
spin-orbit, and the next-to-next leading order fourth post-Newtonian (4PN)
corrections in our analysis. In this way, we could make an accurate examination
of unstable orbits ($3M < r <6M$) of the secondary black hole. We tested the
4PN terms by analyzing the total and radiated energy, compared the
post-Newtonian parameters and the separation of the two black holes for 3PN and
4PN. In conclusion, the 4PN corrections provided a significantly more accurate
tool for analyzing unstable orbits than earlier 3PN terms. Furthermore, in this
paper, we show the gravitational waves emitted by OJ 287 during its complete
orbital evolution including unstable orbits.
