Sparse-representation-based single-channel source separation, which aims to recover each source\'s signal using its corresponding sub-dictionary, has attracted many scholars\' at-tention. The basic premise of this model is that each sub-dic-tionary possesses discriminative information about its corres-ponding source, and this information can be used to recover al-most every sample from that source. However, in a more gene-ral sense, the samples from a source are composed not only of discriminative information but also common information shared with other sources. This paper proposes learning a discri-minative high-fidelity dictionary to improve the separation per-formance. The innovations are threefold. Firstly, an extra sub-dictionary was combined into a conventional union dictionary to ensure that the source-specific sub-dictionaries can capture only the purely discriminative information for their correspond-ing sources because the common information is collected in the additional sub-dictionary. Secondly, a task-driven learning al-gorithm is designed to optimize the new union dictionary and a set of weights that indicate how much of the common informa-tion should be allocated to each source. Thirdly, a source separ-ation scheme based on the learned dictionary is presented. Ex-perimental results on a human speech dataset yield evidence that our algorithm can achieve better separation performance than either state-of-the-art or traditional algorithms.