Diewert (1976) defines an index number as superlative if it is exact for a linearly homogeneous aggregator function or its dual unit cost function that is flexible. The applicability of this definition, however, has been seriously limited by the requirement to identify its exact functional form. This paper interprets the superlative index as its ability to approximate the true economic index number closely to the second order. This interpretation has much more applicability than the original definition and it is virtually the same with the original Diewert's definition in the sense that identification of any particular functional form has no particular value in the index number theory. To prove the usefulness of this interpretation, this paper shows that the quadratic mean of order r index, the unique superlative index number in the original definition and includes such important index numbers as the Fisher, Trnqvist, Walsh as special cases, is also second order approximation to the economic index number.