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Monogamy of entanglement is generally discussed using a bipartiteentanglement measure as an upper bound. Here we discuss a new kind ofmonogamous relation where the upper bound is given by a multipartite measure ofentanglement, the generalized concurrence. We show a new monogamous equalityinvolving the multipartite concurrence, all the bipartite concurrences and thegenuine tripartite entanglement for pure three qubits system. The resultextends to mixed states in an inequality involving the generalized concurrenceand all the bipartite concurrences. We provide a counter-example showing thatthe result cannot be extended for systems with more than three qubits.

Multipartite monogamy of the concurrence