Independent Component Analysis (ICA) is one of the fastest growing fields in the area of neural networks and signal processing. Blind Source Separation (BSS) is one of the applications of ICA. In this paper, ICA has been used for separating unknown source signals. BSS is used to extract independent signal components from their observed linear mixtures at an array of sensors. Various statistical techniques based on information theoretic and algebraic approaches exist for performing ICA. In this paper, we have used an objective function based on independence criterion of the signals. Optimisation of this objective function yields a neural algorithm along with a non-linear function for signal separation. Performance of the algorithm for artificially generated signals as well as audio signals has been evaluated.