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A new model was recently introduced to correct for higher‐order ionospheric residual biases in radio occultation (RO) data. The model depends on the α1 and α2 dual‐frequency bending angle difference squared, and a factor κ, which varies with time, season, solar activity, and height, needing only the F10.7 solar radio flux index as additional background information. To date, this kappa‐correction was analyzed in simulation studies. In this study, we test it on real observed Metop‐A RO data. The goal is to improve the accuracy of monthly mean RO climate records, potentially raising the accuracy of RO data toward higher stratospheric altitudes. We performed a thorough analysis of the kappa‐correction, evaluating its ionospheric sensitivity during the solar cycle for monthly RO climatologies and comparing the kappa‐corrected RO stratospheric climatologies to three other data sets from reanalysis and passive infrared sounding. We find a clear dependence of the kappa‐correction on solar activity, geographic location, and altitude; hence, it reduces systematic errors that vary with the solar cycle. From low to high solar activity conditions, the correction can increase from values of about 0.2 K to more than 2.0 K at altitudes between 40 to 45 km. The correction shifts RO climatologies toward warmer temperatures. With respect to other data sets, however, we found it difficult to draw firm conclusions, because the biases in the other data sets appear to be at similar magnitude as the size of the kappa‐correction. Further validation with more accurate data will be useful. Key Points: The kappa‐correction model is tested for the impact of its correction of higher‐order ionospheric biases in radio occultation dataThe magnitude of the kappa‐correction varies over the solar cycle from 0.2 K to more than 2.0 K at about 40 kmThe correction shifts the stratospheric data toward warmer temperatures; firm validation based on other data sets was difficult [ABSTRACT FROM AUTHOR]