In this paper, we show that some Codd third normal form relations may contain "superfluous" attributes because the definitions of transitive dependency and prime attribute are inadequate when applied to sets of relations. To correct this, an improved third normal form is defined and an algorithm is given to construct a set of relations from a given set of functional dependencies in such a way that the superfluous attributes are guaranteed to be removed. This new normal form is compared with

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... r existing definitions of third normal form, and the deletion normalization method proposed is shown to subsume the decomposition method of normalization.