Statistical topic models have become a useful and ubiquitous text analysis tool for large corpora. One common application of statistical topic models is to support topic-centric navigation and exploration of document collections at the user interface by automatically grouping documents into coherent topics. For today's constantly expanding document collections, topic models need to be updated when new documents become available. Existing work on topic model update focuses on how to best fit the model to the data, and ignores an important aspect that is closely related to the end user experience: topic model stability. When the model is updated with new documents, the topics previously assigned to old documents may change, which may result in a disruption of end users' mental maps between documents and topics, thus undermining the usability of the applications. In this paper, we describe a user-directed non-disruptive topic model update system, nTMU, that balances the tradeoff between finding the model that fits the data and maintaining the stability of the model from end users' perspective. It employs a novel constrained LDA algorithm (cLDA) to incorporate pair-wise document constraints, which are converted from user feedback about topics, to achieve topic model stability. Evaluation results demonstrate advantages of our approach over previous methods.