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Synchronization across different brain regions is suggested to be a possible mechanism for functional integration. Noninvasive analysis of the synchronization among cortical areas is possible if the electrical sources can be estimated by solving the electroencephalography inverse problem. Among various inverse algorithms, spatio-temporal dipole fitting methods such as RAP-MUSIC and R-MUSIC have demonstrated superior ability in the localization of a restricted number of independent sources, and also have the ability to reliably reproduce temporal waveforms. However, these algorithms experience difficulty in reconstructing multiple correlated sources. Accurate reconstruction of correlated brain activities is critical in synchronization analysis. In this study, we modified the well-known inverse algorithm RAP-MUSIC to a multistage process which analyzes the correlation of candidate sources and searches for independent topographies (ITs) among precorrelated groups. Comparative studies were carried out on both simulated data and clinical seizure data. The results demonstrated superior performance with the modified algorithm compared to the original RAP-MUSIC in recovering synchronous sources and localizing the epileptiform activity. The modified RAP-MUSIC algorithm, thus, has potential in neurological applications involving significant synchronous brain activities.