A privacy-preserving Support Vector Machine (SVM) computing scheme is proposed in this paper. Cloud computing has been spreading in many fields. However, the cloud computing has some serious issues for end users, such as unauthorized use and leak of data, and privacy compromise. We focus on templates protected by using a random unitary transformation, and consider some properties of the protected templates for secure SVM computing, where templates mean features extracted from data. The proposed scheme enables us not only to protect templates, but also to have the same performance as that of unprotected templates under some useful kernel functions. Moreover, it can be directly carried out by using well-known SVM algorithms, without preparing any algorithms specialized for secure SVM computing. In the experiments, the proposed scheme is applied to a face-based authentication algorithm with SVM classifiers to confirm the effectiveness.