Abstract: The problem of“tie trees”has been noticed in the traditional Unweighted Pair Group Method with Arithmetic Mean (UPGMA).In order to solve the problem,this paper presents a method of Unweighted Multiple Group Method with Arithmetic Mean (UMGMA),which is an improvement for UPMGA.It has been shown in theory and application that UMGMA can always produce a unique phylogenetic tree.In the case when the UMGMA tree is bifurcating,it must be the same as the eorrespoonding UPGMA tree without considering the order of branches.Differing from UPGMA,UMGMA repeatedly merges multiple groups into one by the vertices of a maximalθ-distant subtree until only one group remains,thus it may produce a multi- furcating tree with a unique topology.By choosing a tolerant parameter properly,UMGMA can be used to construct several unique tolerant multifurcating trees that outline the major branches of a phylogenetic tree on different levels.