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We present a scheme for generation of an entangled state in many spatially separated bimodal cavity modes via cavity quantum electrodynamics. A V-type three-level atom, initially prepared in a coherent superposition of its excited states, successively passes through both the bimodal cavities. If the atom is measured in its ground state after leaving the last cavity, an entangled state of many cavity modes can be generated. The conditions to generate the maximally entangled state with unity probability are worked out.