Abstract: We constructed 4 order unitary matrices by using tensor product based on three classes of 2 order unitary matrices. The results show  that the complete sets of the mutually unbiased bases are still mutually unbiased under four classes  of unitary transformations, but the complete sets of the mutually unbiased bases are no longer mutually unbiased under the other five classes of unitary transformations. The sum of l₁ norm of coherence of Bell-diagonal states under the four-dimensional mutually unbiased bases is no more than 9.

Key words: unitary matrix, mutually unbiased bases, Belldiagonal state,  , l₁ norm of coherence