The design of an arbitrary polygonal invisible cloak is introduced in this paper by considering the different transformation orders. The transformation order is considered as a design variable to achieve the allowable constitutive parameters for a practical cloak with the optimum performance. In the proposed method, a thin layer is removed from the inner cloak boundary to avoid the inevitable singularity at this boundary. Then the transformation order is optimized to achieve the best performance in this truncated cloak. Also, the effect of transformation order in choosing the cloak shield thickness is investigated to design a truncated cloak with better performance.