Support Vector Machine (SVM) has become a very effective method in sta-tistical machine leing and it has proved that training SVM is to solve Nearest Point pairProblem (NPP) between two disjoint closed convex sets. Later Keerthi pointed out that it isdifficult to apply classical excellent geometric algorithms directly to SVM and so designed anew geometric algorithm for SVM. In this article, a new algorithm for geometrically solvingSVM, Kel Projection Algorithm, is presented based on the theorem on fixed-points of pro-jection mapping. This new algorithm makes it easy to apply classical geometric algorithmsto solving SVM and is more understandable than Keerthi’s. Experiments show that the newalgorithm can also handle large-scale SVM problems. Geometric algorithms for SVM, such asKeerthi’s algorithm, require that two closed convex sets be disjoint and otherwise the algo-rithms are meaningless. In this article, this requirement will be guaranteed in theory by usingthe theoretic result on universal kel functions.