  In this paper we show a Cowen-Douglas operator $T \in
\mathcal{B}_{n}(\Omega)$ is the adjoint operator of some backward shift on a
general basis by choosing nice cross-sections of its complex bundle $E_{T}$.
Using the basis theory model, we show that a Cowen-Douglas operator never be a
shift on some Markushevicz basis for $n \ge 2$.
