In this paper, we study the separation of synchronous sources (SSS) problem, which deals with the separation of sources whose phases are synchronous. This problem cannot be addressed through independent component analysis methods because synchronous sources are statistically dependent. We present a two-step algorithm, called phase locked matrix factorization (PLMF), to perform SSS. We also show that SSS is identifiable under some assumptions and that any global minimum of PLMFs cost function is a desirable solution for SSS. We extensively study the algorithm on simulated data and conclude that it can perform SSS with various numbers of sources and sensors and with various phase lags between the sources, both in the ideal (i.e., perfectly synchronous and nonnoisy) case, and with various levels of additive noise in the observed signals and of phase jitter in the sources.