We discuss the necessity of selecting and correcting the observation data on sky brightness along the Sun almucantar at azimuth angles of 2 to 6° presented at the highest confidence level (Level-2) in AERONET tables. To completely exclude the cloud situations and situations with optical inhomogeneities in the atmosphere, the conditions of systematic decrease in angular gradient of brightness with increasing azimuth are to be fulfilled at the first stage. The second stage includes the use of empirical regularities in the brightness angular distribution inferred from the highly accurate observations aimed at elimination of the systematic errors in the experimental data obtained with CIMEL sun photometers. Formulas and tables, necessary for the practical use, are presented.