We report on a search for the radiative decay of Upsilon(1S) to the pseudoscalar mesons eta and eta(') in (21.2 +/- 0.2)x10(6) Upsilon(1S) decays collected with the CLEO III detector at the Cornell Electron Storage Ring. The eta meson was reconstructed in the three modes eta ->gamma gamma, eta ->pi(+)pi(-)pi(0), or eta ->pi(0)pi(0)pi(0). The eta(') meson was reconstructed in the mode eta(')->pi(+)pi(-)eta with eta decaying through any of the above three modes, and also eta(')->gamma rho(0), where rho(0)->pi(+)pi(-). Five out of the seven submodes are found to have very low backgrounds. In four of them we find no signal candidates and in one [Upsilon(1S)->gamma eta('), eta(')->pi(+)pi(-)eta, eta ->pi(+)pi(-)pi(0)] there are two good signal candidates, which is insufficient evidence to claim a signal. The other two submodes (eta ->gamma gamma and eta(')->gamma rho) are background limited, and show no excess of events in their signal regions. We combine the results from different channels and obtain upper limits at the 90% C.L. which are B(Upsilon(1S)->gamma eta)< 1.0x10(-6) and B(Upsilon(1S)->gamma eta('))< 1.9x10(-6). Our limits are an order of magnitude tighter than the previous ones and below the predictions made by some theoretical models.
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