This study develops an innovative approach to homogenize discontinuities in both mean and variance in global subdaily radiosonde temperature data from 1958 to 2018. First, temperature natural variations and changes are estimated using reanalyses and removed from the radiosonde data to construct monthly and daily difference series. A penalized maximal F test and an improved Kolmogorov–Smirnov test are then applied to the monthly and daily difference series to detect spurious shifts in the mean and variance, respectively. About 60% (40%) of the changepoints appear in the mean (variance), and ~56% of them are confirmed by available metadata. The changepoints display a country-dependent pattern likely due to changes in national radiosonde networks. Mean segment length is 7.2 (14.6) years for the mean (variance)-based detection. A mean (quantile)-matching method using up to 5 years of data from two adjacent mean (variance)-based segments is used to adjust the earlier segments relative to the latest segment. The homogenized series is obtained by adding the two homogenized difference series back to the subtracted reference series. The homogenized data exhibit more spatially coherent trends and temporally consistent variations than the raw data, and lack the spurious tropospheric cooling over North China and Mongolia seen in several reanalyses and raw datasets. The homogenized data clearly show a warming maximum around 300 hPa over 30°S–30°N, consistent with model simulations, in contrast to the raw data. The results suggest that spurious changes are numerous and significant in the radiosonde records and our method can greatly improve their homogeneity.