This paper deals with the problem of noise reduction for hands-free communications when two microphones are in use. Recently, forward-and-backward blind source separation (BSS) structures have been suggested to solve acoustic noise reduction and speech enhancement problems. Therefore, we propose a new algorithm that is based on the combination between the dual backward (BSS) structure and the Simplified Fast Transversal Filter (SFTF) algorithm. The obtained results which are expressed in terms of several objective criteria prove and confirm the superiority and the good performances of the proposed dual backward blind SFTF (DBSFTF) in comparison with the classical dual backward normalized least mean square (DBNLMS) algorithm.