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In this work, we introduce a new discriminative training method for nonnegative dictionary learning. The new method can be used in single channel source separation (SCSS) applications. In SCSS, nonnegative matrix factorization (NMF) is used to learn a dictionary (a set of basis vectors) for each source in the magnitude spectrum domain. The trained dictionaries are then used in decomposing the mixed signal to find the estimate for each source. Learning discriminative dictionaries for the source signals can improve the separation performance. To achieve discriminative dictionaries, we try to avoid the bases set of one source dictionary from representing the other source signals. We propose to minimize cross-coherence between the dictionaries of all sources in the mixed signal. We incorporate a simplified cross-coherence penalty using a regularized NMF cost function to simultaneously learn discriminative and reconstructive dictionaries. The new regularized NMF update rules that are used to discriminatively train the dictionaries are introduced in this work. Experimental results show that using discriminative training gives better separation results than using conventional NMF.