Audio source separation is essential for many applications such as hearing aids, telecommunications, and robot audition. Subspace decomposition approaches using polynomial matrix eigenvalue decomposition (PEVD) algorithms applied to the microphone signals, or lower-dimension eigenbeams for spherical microphone arrays, are effective for speech enhancement. In this work, we extend the work from speech enhancement and propose a PEVD subspace algorithm that uses eigenbeams for source separation. The proposed PEVD-based source separation approach performs comparably with state-of-the-art algorithms, such as those based on independent component analysis (ICA) and multi-channel non-negative matrix factorization (MNMF). Informal listening examples also indicate that our method does not introduce any audible artifacts.