The problem of blind audio source separation (BASS) in noisy and reverberant conditions is addressed by a novel approach, termed Global and LOcal Simplex Separation (GLOSS), which integrates full- and narrow-band simplex representations. We show that the eigenvectors of the correlation matrix between time frames in a certain frequency band form a simplex that organizes the frames according to the speaker activities in the corresponding band. We propose to build two simplex representations: one global based on a broad frequency band and one local based on a narrow band. In turn, the two representations are combined to determine the dominant speaker in each time-frequency (TF) bin. Using the identified dominating speakers, a spectral mask is computed and is utilized for extracting each of the speakers using spatial beamforming followed by spectral postfiltering. The performance of the proposed algorithm is demonstrated using real-life recordings in various noisy and reverberant conditions.