This paper proposes a new LMS based and RLS-like algorithms for blind separation of audio signals. The algorithms are developed based on classical adaptive filtering interpretation and modification to the Bussgang cost function, which is one of the main cost functions used in the filed of blind deconvolution. The fast converging RLS algorithm combines both the classical adaptive filtering theory along with the natural gradient rule to implement a more accurate update. This fast converging RLS algorithm is extended for the convolutive blind source separation. The paper also presents simulation results to prove that the new RLS algorithm has a faster convergence speed than the existing natural gradient algorithm.