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We propose a way of including the next-to-leading (NLO) order spin-spincoupling into an effective-one-body (EOB) Hamiltonian. This work extends [S.Balmelli and P. Jetzer, Phys. Rev. D 87, 124036 (2013)], which is restricted tothe case of equatorial orbits and aligned spins, to general orbits witharbitrary spin orientations. This is done applying appropriate canonicalphase-space transformations to the NLO spin-spin Hamiltonian inArnowitt-Deser-Misner (ADM) coordinates, and systematically adding "effectiv"quantities at NLO to all spin-squared terms appearing in the EOB Hamiltonian.As required by consistency, the introduced quantities reduce to zero in thetest- mass limit. We expose the result both in a general gauge and in agauge-fixed form. The last is chosen such as to minimize the number of newcoefficients that have to be inserted into the effective spin squared. As aresult, the 25 parameters that describe the ADM NLO spin-spin dynamics getcondensed into only 12 EOB terms.

Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling