Although　a　number　of　normalized　edit　distances　presented　so　far　may　offer　good　performance　in　some　applications,　none　of　them　can　be　regarded　as　a　genuine　metric　between　strings　because　they　do　not　satisfy　the　triangle　inequality.　Given　two　strings　X　and　Y　over　a　finite　alphabet,　this　paper　defines　a　new　normalized　edit　distance　between　X　and　Y　as　a　simple　function　of　their　lengths　(vertical　bar　X　vertical　bar　and　vertical　bar　Y　vertical　bar)　and　the　Generalized　Levenshtein　Distance　(GLD)　between　them.　The　new　distance　can　be　easily　computed　through　GLD　with　a　complexity　of　O(vertical　bar　X　vertical　bar　(.)　vertical　bar　Y　vertical　bar)　and　it　is　a　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　having　the　same　weight.　Experiments　using　the　AESA　algorithm　in　handwritten　digit　recognition　show　that　the　new　distance　can　generally　provide　similar　results　to　some　other　normalized　edit　distances　and　may　perform　slightly　better　if　the　triangle　inequality　is　violated　in　a　particular　data　set.