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Privacy preservation is important for machine learning and data mining, but measures designed to protect private information often result in a trade-off: reduced utility of the training samples. This paper introduces a privacy preserving approach that can be applied to decision tree learning, without concomitant loss of accuracy. It describes an approach to the preservation of the privacy of collected data samples in cases where information from the sample database has been partially lost. This approach converts the original sample data sets into a group of unreal data sets, from which the original samples cannot be reconstructed without the entire group of unreal data sets. Meanwhile, an accurate decision tree can be built directly from those unreal data sets. This novel approach can be applied directly to the data storage as soon as the first sample is collected. The approach is compatible with other privacy preserving approaches, such as cryptography, for extra protection.