We clarify the essence of the method proposed by You (Phys. Rev. Lett. 90 (2004) 030402) to create the maximally entangled atomic N-GHZ state in the Mott insulator state. Based on the time-independent perturbation theory,we find that the validity of the method can be summarized as that the Hamiltonian goveing the evolution is approximately equivalent to the type aJ2x + bJx, which is the well known form used to create the maximally entangled state.