Software product line (SPL) is an approach used to develop a range of software products with a high degree of similarity. In this approach, a feature model is usually used to keep track of similarities and differences. Over time, as modifications are made to the SPL, inconsistencies with the feature model could arise. The first approach to dealing with these inconsistencies is refactoring. Refactoring consists of small steps which, when accumulated, may lead to large-scale changes in the SPL, resulting in features being added to or eliminated from the SPL. In this paper, we propose a framework for refactoring SPLs, which helps keep SPLs consistent with the feature model. After some introductory remarks, we describe a formal model for representing the feature model. We express various refactoring patts applicable to the feature model and the SPL formally, and then introduce an algorithm for finding them in the SPL. In the end, we use a real-world case study of an SPL to illustrate the applicability of the framework introduced in the paper.