This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA), and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyses of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results. This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA) and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyzes of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results.