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In this paper, we study the Ma-Trudinger-Wang (MTW) conditions for costfunctions $c$ which are of the form $c=l\circ d$, where $d$ is a Riemanniandistance function with constant sectional curvature. In this case, the MTWconditions are equivalent to some computable conditions on the function $l$. Asa corollary, we give some new costs on Riemannian manifolds of constantnegative curvature for which the MTW conditions are satisfied.

New examples on spaces of negative sectional curvature satisfying Ma-Trudinger-Wang conditions