Based on the equilibrium manifold of nonlinear system, the influence of mapping choice on equilibrium manifold expansion results for a class of nonlinear systems which parametric dynamic matrix rank is not full is discussed. Considering different mapping choices with different equilibrium manifold expansion model errors, the conditions of equilibrium manifold expansion without form error for nonlinear system are given. Compared with single input system, the mapping choices which make the equilibrium manifold expansion meaningless for multi-input system are discussed. The simulation results show that the above mentioned theories are effective.