A thorough study and error analysis was made of the Van den Akker or "auxiliary sphere" method of determining a scale of directional-hemispherical reflectance factor. The effects of a non-Lambertian distribution of the reflected radiation, including retroreflection, were included in this study. Three working standards were measured to an uncertainty in reflectance of less than ±0.0015 and these will be used as a basis for a new, more accurate NBS scale of 6°-hemispherical reflectance factor. The new scale and the NBS scale established in 1965 are in agreement to within the uncertainty of ±0.005 assigned to the 1965 scale.