Separating audio sources from a convolutive mixture of signals from various independent sources is a very fascinating area in personal and professional context. The task of source separation becomes trickier when there is no idea about mixing environment and can be termed as blind audio source separation (BASS). Mixing scenario becomes more complicated when there is a difference between number of audio sources and number of recording microphones, under determined and over determined mixing. The main challenge in BASS is quality of separation and separation speed and the convergence speed gets compromised when separation techniques focused on quality of separation. This work proposed divergence algorithm designed for faster convergence speed along with good quality of separation. Experiments are performed for critically determined audio recording, where number of audio sources is equal to number of microphones and no noise component is taken into consideration. The result advocates that the modified convex divergence algorithm enhance the convergence speed by 20-22% and good quality of separation than conventional convex divergence ICA, Fast ICA, JADE.