This paper deals with single-channel speech separation. First, it is proved that when the sparse bases of the signal sources satisfy certain conditions, all the sources can be perfectly separated from a single mixture by l0 optimization. Then, a special case where the single mixture is generated by two independent speech sources is studied in more detail. It is revealed that the ideal quasi- KLT bases constructed from the original sources satisfy the sufficient conditions for perfect separation of mixed signals. Considering the fact that the ideal quasi-KLT bases cannot be obtained in practice, template-matching based quasi- KLT bases generated from the single mixture are also proposed to perform single-channel speech separation. Finally, simulation results demonstrating the effective performance of single-channel separation of two speech sources by l0 optimization using the template-matching based quasi-KLT bases are presented.