Determining　optimum　cluster　number　is　a　key　research　topic　included　in　cluster　validity,　a　fundamental　problem　unsolved　in　cluster　analysis.　In　order　to　determine　the　optimum　cluster　number,　this　article　proposes　a　new　cluster　validity　function　for　two-dimension　datasets　theoretically　based　on　geometric　probability.　The　function　makes　use　of　the　corresponding　relationship　between　a　two-dimension　dataset　and　the　related　two-dimension　discrete　point　set　to　measure　the　cluster　structure　of　the　dataset　according　to　the　distributive　feature　of　the　point　set　in　the　characteristic　space.　It　is　designed　from　the　perspective　of　intuition　and　thus　easily　understood.　Through　TM　remote　sensing　image　classification　examples,　compare　with　the　supervision　and　unsupervised　classification　in　ERDAS　and　the　cluster　analysis　method　based　on　geometric　probability　in　two-dimensional　square,　which　is　proposed　in　literature　2.　Results　show　that　the　proposed　method　can　significantly　improve　the　classification　accuracy.