In pairwise comparisons, several scales are used to compare objects. Perhaps the most known is Saaty’s fundamental scale for the AHP/ANP from 1 to 9 (with reciprocals), but other scales with 3, 5 or 10 items are also used in practice. Since the AHP/ANP is scale invariant, the following problem arises: for example, a preference of one object over other object expressed by the value 2 means something else for the scale from 1 to 3 (it expresses the medium preference) and the scale from 1 to 100 (in this case the preference is almost negligible). Therefore, the need of a normalization for pairwise comparison scales arises. The aim of the article is to propose a suitable transformation of a general linear scale for pairwise comparisons to a unit real interval that preserves several natural and desirable properties.