We investigate the monogamy nature of entanglement in a three-qubit system. A monogamy inequality ispresented to describe the exclusive relation between the A-B two-qubit concurrence CAB and the AB-C three-qubit concurrence C(AB)c, which represents the entanglement between qubits A and B as a whole and the thirdqubit C. It is found that the entanglement between any two qubits in a three-qubit system is limited by theentanglement between these two qubits and another qubit. As a consequence, we present the upper bounds forthe concurrence CAB, when the concurrence between qubits A and C (C_(AC))and the concurrence between qubitsB and C (CBc) are both given or one of the two is provided.
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