We describe a novel binary classification technique called Banded SVM (B-SVM). In the standard C-SVM formulation of Cortes et al. (1995), the decision rule is encouraged to lie in the interval [1, \infty]. The new B-SVM objective function contains a penalty term that encourages the decision rule to lie in a user specified range [\rho_1, \rho_2]. In addition to the standard set of support vectors (SVs) near the class boundaries, B-SVM results in a second set of SVs in the interior of each class.