Many problems require making sequential decisions. For these problems, the benefit of acquiring further information must be weighed against the costs. In this paper, we describe the catenary support vector machine (catSVM), a margin-based method to solve sequential stopping problems. We provide theoretical guarantees for catSVM on future testing examples. We evaluated the performance of catSVM on UCI benchmark data and also applied it to the task of face detection. The experimental results show that catSVM can achieve a better cost tradeoff than single-stage SVM and chained boosting.