We propose a privacy-preserving machine learning scheme with encryption-then-compression (EtC) images, where EtC images are images encrypted by using a block-based encryption method proposed for EtC systems with JPEG compression. In this paper, a novel property of EtC images is first discussed, although EtC ones was already shown to be compressible as a property. The novel property allows us to directly apply EtC images to machine learning algorithms non-specialized for computing encrypted data. In addition, the proposed scheme is demonstrated to provide no degradation in the performance of some typical machine learning algorithms including the support vector machine algorithm with kernel trick and random forests under the use of z-score normalization. A number of facial recognition experiments with are carried out to confirm the effectiveness of the proposed scheme.