For the fixed orthonormal basis, the design of the determinate measurement matrix is investigated by using the incoherence criterion between the measurement matrix and the sparse basis. The smaller the coherence between the measurement matrix and the sparse basis is, the less the required measurement number in the process of compressed sampling is, the more information in the original signal will be contained, and the higher the probability of restructure is. According to the definition of coherence between the measurement matrix and the sparse basis, the minimax method of satisfying optimal incoherence is constructed for the fixed known orthonormal basis, furthermore, the measurement matrix that is most incoherent with the orthonormal basis can be found. Finally, to verify the effectiveness of the method mentioned in this paper, the comparison, between a numerical simulation example of taking the fixed orthonormal basis as a discrete cosine basis and the coherence corresponding to the common measurement matrices, is made.