This paper discusses the problem of acoustic noise reduction and speech enhancement through the forward blind source separation structure. Recently we have proposed a new combination between the forward blind source separation structure and the fast normalized least mean square algorithm that provides an efficient dual algorithm for noise reduction and speech enhancement applications. In this paper we propose a new subband implementation of this recent dual algorithm, this last allows improving the speed convergence behavior of the previous proposed algorithm in its fullband form. The performance of the proposed dual subband algorithm is compared with its fullband version of the dual fast normalized least mean square algorithm and the classical fullband dual normalized least mean square algorithm, and the two channel subband forward algorithm in terms of several objective criteria. The obtained results show the good performances of the proposed dual subband algorithm.