Past stratospheric ozone depletion has acted to cool the Earth's surface. As the result of the phase-out of anthropogenic halogenated compounds emissions, stratospheric ozone is projected to recover and its radiative forcing (RF-O3 ~ −0.05 W/m2 presently) might therefore be expected to decay in line with ozone recovery itself. Using results from chemistry-climate models, we find that, although model projections using a standard greenhouse gas scenario broadly agree on the future evolution of global ozone, they strongly disagree on RF-O3 because of a large model spread in ozone changes in a narrow (several km thick) layer, in the northern lowermost stratosphere. Clearly, future changes in global stratospheric ozone cannot be considered an indicator of its overall RF. The multi-model mean RF-O3 estimate for 2100 is +0.06 W/m2 but with a range such that it could remain negative throughout this century or change sign and reach up to ~0.25 W/m2.