Many algorithms have been designed to discover community structure in networks. Most of these detect disjoint communities, while a few can find communities that overlap. We propose a new, two-phase, method of detecting overlapping communities. In the first phase, a network is transformed to a new one by splitting vertices, using the idea of split betweenness; in the second phase, the transformed network is processed by a disjoint community detection algorithm. This approach has the potential to convert any disjoint community detection algorithm into an overlapping community detection algorithm. Our experiments, using several "disjoint" algorithms, demonstrate that the method works, producing solutions, and execution times, that are often better than those produced by specialized "overlapping" algorithms.