Based on a recently presented generic broadband blind source separation (BSS) algorithm for convolutive mixtures, we propose in this paper a novel algorithm combining advantages of broadband algorithms with the computational efficiency of narrowband techniques. By selective application of the Szegö theorem which relates properties of Toeplitz and circulant matrices, a new normalization is derived as a special case of the generic broadband algorithm. This results in a computationally efficient and fast converging algorithm without introducing typical narrowband problems such as the internal permutation problem or circularity effects. Moreover, a novel regularization method for the generic broadband algorithm is proposed and subsequently also derived for the proposed algorithm. Experimental results in realistic acoustic environments show improved performance of the novel algorithm compared to previous approximations.