Abstract: Based on the ideas of Osuna algorithm (Osuna E., 1997) and SMO algorithm (Platt, J., 1998a, Platt, J., 1998b), this paper suggests a new algorithm for training SVMs called 3SAO (Ternary Sequential Analytic Optimization). 3SAO breaks the original large QP problem of training SVMs into sequential sub-QP problems. Each sub-QP involves three Lagrange multipliers and is analytically solved. Based on the observation that optimizing steps involving bound Lagrange multipliers often give more contribution to the value of objective function than steps involving only non-bound Lagrange multipliers do, 3SAO uses an effective but extremely simple set of heuristics for choosing multipliers. The result of our tests on two benchmark datasets proves that 3SAO converges remarkably faster than Keerthi`s improved SMOs(Keerthi., 2001) in most situations.