An algorithm for target speech enhancement based on degenerate unmixing and estimation technique (DUET) is described. Although the DUET can accomplish source separation only from two mixtures, the requirements of knowing the number of sources in advance and of estimating the attenuation and delay parameters for all sources prevent it from being used in real-world applications. Circumventing these requirements, the described algorithm is useful for speech enhancement where only one target speech should be extracted. Experimental results show that the algorithm provides much faster convergence of all the required parameters and noise suppression performances that are better than or comparable to the DUET with negligible distortion of the recovered speech.