In order to improve the performance of a speech enhancement system, Plapous introduced a novel method called two-step noise reduction (TSNR) technique to refine the a priori SNR estimation of the decision-directed (DD) approach. However, the performance of this method depends on the choice of gain function. In this paper, we propose a modified approach for the a priori SNR estimation in DCT domain with two steps like the TSNR method. While in the second step, the proposed approach computes directly the square of clean speech component using the estimated a priori SNR of the DD approach, its result is not restricted on the gain function, and thus the drawback of the TSNR method is removed while the advantages are kept. A number of objective tests under various conditions are provided, and the results show the improved performance of our approach.