This letter presents a two-stage method to extend the degenerate unmixing estimation technique (DUET) for reverberant speech separation. First, frequency-bin-wise attenuation and delay parameters are introduced and estimated by online update rules, to handle early reflections. Next, a mask reestimation algorithm based on the precedence effect is developed to detect and fix the errors on binary masks caused by late reflections. Experimental results demonstrate that the proposed method improves separation performance significantly.