Data products from the Cloud-Aerosol Lidar with Orthogonal Polarization (CALIOP) on board Cloud-Aerosol Lidar and Infrared Pathfinder Satellite Observations (CALIPSO) were recently updated following the implementation of new (version 4) calibration algorithms for all of the level 1 attenuated backscatter measurements. In this work we present the motivation for and the implementation of the version 4 nighttime 532 nm parallel channel calibration. The nighttime 532 nm calibration is the most fundamental calibration of CALIOP data, since all of CALIOP's other radiometric calibration procedures - i.e., the 532 nm daytime calibration and the 1064 nm calibrations during both nighttime and daytime - depend either directly or indirectly on the 532 nm nighttime calibration. The accuracy of the 532 nm nighttime calibration has been significantly improved by raising the molecular normalization altitude from 30-34 km to 36-39 km to substantially reduce stratospheric aerosol contamination. Due to the greatly reduced molecular number density and consequently reduced signal-to-noise ratio (SNR) at these higher altitudes, the signal is now averaged over a larger number of samples using data from multiple adjacent granules. As well, an enhanced strategy for filtering the radiation-induced noise from high energy particles was adopted. Further, the meteorological model used in the earlier versions has been replaced by the improved MERRA-2 model. An aerosol scattering ratio of 1.01 ± 0.01 is now explicitly used for the calibration altitude. These modifications lead to globally revised calibration coefficients which are, on average, 2-3% lower than in previous data releases. Further, the new calibration procedure is shown to eliminate biases at high altitudes that were present in earlier versions and consequently leads to an improved representation of stratospheric aerosols. Validation results using airborne lidar measurements are also presented. Biases relative to collocated measurements acquired by the Langley Research Center (LaRC) airborne high spectral resolution lidar (HSRL) are reduced from 3.6% ± 2.2% in the version 3 data set to 1.6% ± 2.4 % in the version 4 release.