The delta values of the isotope composition of atmospheric ozone is ~100‰ (referenced to atmospheric O2). Previous photochemical models, which considered the isotope fractionation processes from both formation and photolysis of ozone, predicted δ49O3 and δ50O3 values, in δ49O3 versus δ50O3 space, that are >10‰ larger than the measurements. We propose that the difference between the model and observations could be explained either by the temperature variation, Chappuis band photolysis, or a combination of the two and examine them. The isotopic fractionation associated with ozone formation increases with temperature. Our model shows that a hypothetical reduction of ~20 K in the nominal temperature profile could reproduce the observations. However, this hypothesis is not consistent with temperatures obtained by in situ measurements and NCEP Reanalysis. Photolysis of O3 in the Chappuis band causes O3 to be isotopically depleted, which is supported by laboratory measurements for 18O18O18O but not by recent new laboratory data made at several wavelengths for 49O3 and 50O3. Cloud reflection can significantly enhance the photolysis rate and affect the spectral distribution of photons, which could influence the isotopic composition of ozone. Sensitivity studies that modify the isotopic composition of ozone by the above two mechanisms are presented. We conclude isotopic fractionation occurring in photolysis in the Chappuis band remains the most plausible solution to the model-observation discrepancy. Implications of our results for using the oxygen isotopic signature for constraining atmospheric chemical processes related to ozone, such as CO2, nitrate, and the hydroxyl radical, are discussed.