  We present a combinatorial structure of generators of $D(\mathcal{A}).$ This
structure permits us to detect the relationship between the combinatorial
determined property and the singularity of vector field. Consequently, by using
only combinatorial data, we have a basis of the module in free case and that
yields a proof for the Terao's conjecture. We also verify the example of
Ziegler and give a sufficient condition on combinatorial determined property of
generators.
