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Non-negative matrix factorization (NMF) is a dimensionality reduction method that usually leads to a part-based representation, and it is shown to be effective for source separation. However, the performance of the source separation degrades when one signal can be described with the bases for the other source signals. In this paper, we propose a discriminative NMF (DNMF) algorithm which exploits the reconstruction error for the other signals as well as the target signal based on target bases. The objective function to train the basis matrix is constructed to reward high reconstruction error for the other source signals in addition to low reconstruction error for the signal from the corresponding source. Experiments showed that the proposed method outperformed the standard NMF by about 0.26 in perceptual evaluation of speech quality score and 1.95 dB in signal-to-distortion ratio when it is applied to speech enhancement at input SNR of 0 dB.