Since the creation of the spatially oriented format for acoustics (SOFA, Audio Engineering Society standard AES69), numerous databases of head-related transfer functions (HRTFs) are now available as standardized SOFA files. However, the methodologies for measuring and postprocessing HRTFs vary significantly across laboratories. This leads to objective and perceptual inconsistencies between HRTF databases and makes it challenging to integrate multiple databases into a single repository to facilitate wide-scale research and application. This paper introduces a normalization procedure, applicable to any HRTF data set, aimed at enhancing the consistency across HRTF data sets obtained from different laboratories while preserving the spatial information essential to HRTFs. The proposed approach consists of six processing steps: low-pass filtering, temporal alignment, temporal windowing, diffuse-field equalization, low-frequency extrapolation, and far-field correction. The normalization was evaluated on 17 HRTF data sets of the same dummy head by means of acoustic analyses and auditory simulations and further validated with respect to a database of 54 human subjects. Results show that the proposed normalization improves data set applicability and consistency while maintaining the directional cues within each data set.