The EEG source localization is an ill-posed problem. It involves estimation of the sources which outnumbers the number of measurements. For a given measurement at given time all sources are not active which makes the problem as sparse inversion problem. This paper presents a new approach for dense array EEG source localization. This paper aims at reducing the solution space to only most certain sources and thereby reducing the problem of ill-posedness. This employs a two-stage method where the first stage finds the most certain sources that are likely to produce the observed EEG by using a statistical measure of sources, the second stage solves the inverse problem by restricting the solution space to only most certain sources and their neighbors. This reduces the solution space for other source localization methods hence improvise their accuracy in localizing the active neurological sources in the brain which is the main goal. This method has been validated and applied to real 256 channel data and the results were analyzed.