  The canonical Arnowitt-Deser-Misner (ADM) Hamiltonian with next-to-leading
order spin-spin coupling [J. Steinhoff, S. Hergt, and G. Sch\"afer] is
converted into the EOB formalism of T. Damour, P. Jaranowski, and G. Sch\"afer
for the special case of spinning black hole binaries whose spins are aligned
with the angular momentum. In particular, we propose to include the new terms
by adding a dynamical term of next-to-leading order to the Kerr parameter
squared entering the effective metric. The modified EOB Hamiltonian
consistently reduces to the Kerr Hamiltonian as the mass ratio tends to zero;
moreover, it predicts the existence of an Innermost Stable Circular Orbit. We
also derive, for the general case of arbitrarily oriented spins but in the
vanishing mass-ratio limit, a coordinate transformation that maps the
next-to-leading order spin-spin contribution of the ADM Hamiltonian to the EOB
Hamiltonian.
