In this paper, we propose an improvement to the method of combined segmentation verification for multi-script signature verification. In our previous paper, we proposed generalized segmentation verification (GSV) for multi-script signature verification and evaluated the method using the SigComp dataset. GSV improved the performance of multi-script signature verification by introducing a two-stage strategy in which, during the second stage, the support vector machine (SVM) evaluated matching scores that were derived by signature verifiers during the first stage. For this strategy, the SVM was trained using a dataset that consisted of genuine and skilled-forgery verification scores calculated from signatures of third persons, whose signatures were not registered in the system. However, it was difficult to prepare skilled-forgery signatures even though the method required third-person signatures. Our proposed multi-script signature verification method uses a training dataset that contains no skilled-forgery signatures. This method uses the genuine signatures of third persons as training samples of the forgery class for SVM training. We also introduce an effective sampling method that uses a one-class SVM to reduce the sample number for the training dataset. The results of evaluation experiments using the SigComp multi-script signature dataset show that the performance of the proposed method is competitive with that of the method trained with a skilled-forgery dataset for multi-script signature verification.