Conventional time-frequency-domain blind source separation (BSS) requires permutation alignment of the sound sources. Permutation alignment methods can be classified into two types: those that use the direction of arrival (DOA) constraints and those that model the sound source characteristics instead of DOA constraints. Multi-channel non-negative matrix factorization (MNMF), which is based on the second type, is one of the most effective BSS methods. However, our experiments revealed that its permutation alignment sometimes fails due to the lack of a DOA constraint. We present a permutation alignment method based on the DOAs directly obtained from a spatial correlation matrix by using multiple signal classification (MUSIC) and that solves the permutation problems by minimizing the discrepancy of the MUSIC spectra, which belong to the same source, in the middle of the BSS algorithm. Our proposed method boosts the second type with a help of the DOA constraint and can be applied in a blind manner to both the mixing system approach, e.g., MNMF, and the demixing system approach, e.g., independent low-rank matrix analysis. Experiments showed that the proposed method is effective for both approaches.