Heavy oxygen isotope enrichment in stratospheric CO2 has been identified in the past as a direct result of the large O3 isotope anomaly though no simultaneous measurements are known. Results from 8 stratospheric balloon flights at two latitudes are reported that provide now a complete oxygen isotope analysis of both gases. An unambiguous, very tight correlation between enrichments of 17O and 18O in CO2 has been found. The large ratio δ17O/δ18O of 1.71 ¿ 0.03 shows a faster transfer of 17O than of 18O into CO2 and establishes a standard throughout the lower and middle stratosphere between midlatitudes and high northern latitudes. Ozone isotope transfer can now be treated in models with reliable atmospheric data.