This paper presents a novel reject rule for support vector classifiers, based on the receiver operating characteristic (ROC) curve. The rule minimises the expected classification cost, defined on the basis of classification and the error costs for the particular application at hand. The rationale of the proposed approach is that the ROC curve of the SVM contains all of the necessary information to find the optimal threshold values that minimise the expected classification cost. To evaluate the effectiveness of the proposed reject rule, a large number of tests has been performed on several data sets, and with different kernels. A comparison technique, based on the Wilcoxon rank sum test, has been defined and employed to provide the results at an adequate significance level. The experiments have definitely confirmed the effectiveness of the proposed reject rule.