  We introduce a monogamy inequality for quantum correlations, which implies
that the sum of pairwise quantum correlations is upper limited by the amount of
multipartite quantum correlations as measured by the global quantum discord.
This monogamy bound holds either for pure or mixed quantum states provided that
bipartite quantum discord does not increase under discard of subsystems. We
illustrate the monogamy behavior for multipartite pure states with Schmidt
decomposition as well as for W-GHZ mixed states. As a by-product, we apply the
monogamy bound to investigate residual multipartite correlations.
