We present a novel solution to the problem of localization of MEG and EEG brain signals. The solution is sequential and iterative, and is based on minimizing the least-squares (LS)criterion by the Alternating Projection (AP) algorithm, which is well known in the context of array signal processing. Unlike existing scanning solutions belonging to the beamformer and multiple-signal classification (MUSIC) families, the algorithm has good performance in low signal-to-noise ratio (SNR) and can cope with closely spaced sources and any mixture of correlated sources. Results from simulated and experimental MEG data from a real phantom demonstrated robust performance across an extended SNR range, the entire inter-source correlation range, and across multiple sources, with consistently superior localization accuracy than popular scanning methods.