Aimed at the stability of calibration coefficients in a general non-orthogonal retrieval algorithm (NRA) of pure rotational Raman lidars (PRRLs), an orthogonal retrieval algorithm (ORA) of atmospheric temperature profiles based on the orthogonal basis function is proposed. This algorithm eliminates the correlation between the calibration coefficients in the NRA to reduce the influence of the number of calibration points and the selection scheme on the calibration coefficients. In this paper, the stabilities of calibration coefficients in the NRA and ORA are compared and analyzed, and the data analysis for atmospheric temperature profiles with a time resolution of minute-level are given, based on the developed Cloud Precipitation Potential Evaluation (CPPV) lidar data and the parallel radiosonde temperature data. The analysis results show that coefficients of variation (CVs) of ORA calibration coefficients are one order of magnitude smaller than those of NRA coefficients. The mean deviation of the ORA retrieval results is roughly reduced by 16.1% compared with the NRA, and the root-mean-square deviation is roughly reduced by 15.0% compared with the NRA. Therefore, the temperature retrieval performance of the ORA is better than that of the NRA.