A potential scheme is proposed for generating cluster states of many atoms in cavity quantum electradynamics (QED), in which an unorthodox encoding is employed with the ground state being qubit |0> while two closely spaced upper states being qubit |1>. Throughout the scheme the cavities can be in thermal states but are only virtually excited. We show how to create the cluster states by performing a two-step but no single-qubit operation. Discussion is also carried out on the experimental feasibility of our scheme.
