Global Positioning System radio occultation (GPS RO) measurements have been shown to be valuable for climate monitoring. The refractivity retrieved from these measurements are most accurate below 25 km altitude. At higher altitudes, the atmosphere becomes increasingly tenuous, and the measurement noise becomes comparable to or exceeds the bending signal. This necessitates some form of smoothing or modeling of the bending angles at high altitudes before Abel inversion. In this paper, we introduce a new approach to reduce the systematic bias that could result from such highaltitude initialization. We show that the climatological average of refractivity can be computed as the Abel inversion of the average bending angles with very little error in the stratosphere. By using the average bending angles, we can substantially reduce the random noise in the measurements and increase the altitude at which the initialization needs to be applied. We performed a simulation study which validated this approach and demonstrated the significant improvement in stratospheric refractivity retrieval. Applying the method to actual COSMIC data showed a similar level of difference between our method and the conventional method above 25 km. This implies that the improvement seen in the simulation could be achievable with the real data.