Abstract: Using a simple function of the sizes of two trees and the edit distance between them,this paper presents a normalized tree edit distance,which not only satisfies the triangle inequality,but also is a genuine metric valued in 0,1 under the condition that the weight function is a metric over the set of elementary edit operations with all costs of insertions/deletions of the same weight.Moreover,the distance can be directly computed through tree edit distances and it has the same computing time complexity with the tree edit distance.Handwritten digits recognition experiments show that the metric normalization can reach 91.6%,which is 0.2% and 0.8% better than that of the other two existing methods respectively when the AESA is used.