  In this paper, we show that there are eight distinct forms of the
Greenberger-Horne-Zeilinger (GHZ) argument for the four-qubit cluster state
$|\phi_4>$ and forty eight distinct forms for the five-qubit cluster state
$|\phi_5>$ in the case of the one-dimensional lattice. The proof is obtained by
regarding the pair qubits as a single object and constructing the new
Pauli-like operators. The method can be easily extended to the case of the
N-qubit system and the associated Bell inequalities are also discussed.
Consequently, we present a complete construction of the GHZ theorem for the
cluster states of N-qubit in the case of the one-dimensional lattice.
