In this paper, we present a new global error bound for the dual formulation of the support vector machine (SVM) whose penalty terms are measured by 2-norm (L2-SVM). An further formulation in which an additional term is added to the objective function is also considered (SCL2-SVM). A global error bound for the dual of the latter problem is derived. This error bound is used to identify those constraints of primal SCL2-SVM that will be active at the solution. The correct identification of active constraints is important to find the support vectors and to build the working set of most iterative algorithms for SVM. Computational results are presented showing that the proposed method is able to quickly identify a large percentage of constraints that are active at the optimal solution.