The　traditional　UPGMA　(Unweighted　Pair　Group　Method　with　Arithmetic　Mean)　sometimes　derives　two　or　more　topologies　of　＇tie　trees＇　from　a　single　data　set,　depending　on　the　order　of　data　entry.　This　paper　presents　an　improved　algorithm　for　UPGMA,　namely,　UMGMA　(Unweighted　Multiple　Group　Method　with　Arithmetic　Mean),　which　can　produce　a　unique　multifurcating　tree　from　any　distance　matrix.　Moreover,　a　UMGMA　tree　has　the　same　topology　as　its　corresponding　UPGMA　tree　if　it　is　actually　bifurcating.　UMGMA　is　different　from　UPGMA　in　that　it　repeatedly　merges　multiple　groups　into　one　by　the　vertices　of　a　maximal　a-distant　subtree　until　only　one　group　is　left,　so　the　UMGMA　tree　is　always　unique　even　in　the　case　that　the　UPGMA　tree　is　not　unique.　©　2010　IEEE.