In this paper,the authors start with the introduction of generalized FD path and external closure.With the application of them,they show that the number of closures are reduced when calculating the nonredundant cover of a given functional dependency set.Then a new 3NF synthesis algorithm is presented.In this algorithm,the calculation of nonredundant cover in 3NF synthesis is reduced from two passes to one.So the total number of closures that to be calculated are significantly reduced.