Y2O3 codoped with Bi3+ and Yb3+ is considered as an efficient downconversion material combining strong broadband absorption of Bi3+ with photon splitting by cooperative energy transfer from Bi3+ to two Yb3+ neighbors. However, evidence for photon splitting is lacking. Here we investigate the Bi3+-to-Yb3+ energy-transfer mechanism. For cooperative energy transfer the Yb3+-concentration-dependent luminescence decay will show clear characteristics of cooperative dipole-dipole transfer. Analysis of Yb3+-concentration and temperature-dependent decay curves however demonstrates that the energy-transfer mechanism is not cooperative but single step, probably through a Bi4+-Yb2+ charge-transfer state. The temperature dependence of the Bi3+-to-Yb3+ energy-transfer efficiency is unusual as it decreases with temperature, unlike commonly observed thermally activated energy transfer. This is a signature of energy transfer via exchange interaction. The present results provide evidence for the absence of photon splitting in Y2O3:Bi3+,Yb3+ and form a convincing demonstration of exchange interaction mediated energy transfer.