Privacy-preserving decision tree mining is an important problem that has yet to be thoroughly understood. In fact, the privacypreserving decision tree mining method explored in the pioneer paper [1] was recently showed to be completely broken, because its data perturbation technique is fundamentally flawed [2]. However, since the general framework presented in [1] has some nice and useful features in practice, it is natural to ask if it is possible to rescue the framework by, say, utilizing a different data perturbation technique. In this paper, we answer this question affirmatively by presenting such a data perturbation technique based on random substitutions. We show that the resulting privacy-preserving decision tree mining method is immune to attacks (including the one introduced in [2]) that are seemingly relevant. Systematic experiments show that it is also effective.