In this paper, we determine all the nondegenerate Darboux matries of first order for quite general 1+1 dimensional unreduced Lax pairs, in which the potentials can be arbitrary rational functions of the spectral parameter. An explicit way to get Darboux matrix in terms of its initial value and the fundamental solution of the Lax pair is provided. Also, the permutability property of the Darboux matrices is obtained by twice Darboux transformations.

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