We report the results of the first search for the decay B-s(0) -> eta'eta using 121.4 fb(-1) of data collected at the Upsilon(5S) resonance with the Belle detector at the KEKB asymmetric-energy e(+)e(-) collider. We observe no significant signal and set a 90% confidence-level upper limit of 6.5 x 10(-5) on the branching fraction of this decay.