A new neural-network adaptive algorithm is proposed for performing extraction of independent source signals from a linear mixture of them. Using a suitable nonlinear Hebbian learning rule and a new deflation technique, the developed neural network is able to extract the source signals (sub-Gaussian and/or super-Gaussian) one-by-one with specified order according to their stochastic properties, namely, in decreasing order of absolute normalised kurtosis. The validity and performance of the algorithm are confirmed through extensive computer simulations.