Scale-free networks have strong tolerance against random failures yet are fragile under intentional attacks. Existing results show that the network robustness can also be affected by its correlation profile. Specifically, scale-free networks with larger assortativity coefficients generally tend to be more robust against intentional attack. In this letter, we reveal some interesting different observations. By proposing a simple rewiring method which does not change any nodal degree, we show that

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... network robustness can be steadily enhanced at a slightly decreased assortativity coefficient. The tolerance against random failures meanwhile remains largely unaffected. Such observations demonstrate the more complicated relationship between network robustness and its assortativity level, as well as some new possibilities of network enhancement and protection.