The radial basis function (RBF) approach has been used to improve the mass predictions of nuclear models. However, systematic deviations exist between the improved masses and the experimental data for nuclei with different odd-even parities of ($Z$, $N$), i.e., the (even $Z$, even $N$), (even $Z$, odd $N$), (odd $Z$, even $N$), and (odd $Z$, odd $N$). By separately training the RBF for these four different groups, it is found that the systematic odd-even deviations can be cured in a large extend and the predictive power of nuclear mass models can thus be further improved. Moreover, this new approach can better reproduce the single-nucleon separation energies. Based on the latest version of Weizsacker-Skyrme model WS4, the root-mean-square deviation of the improved masses with respect to known data falls to $135$ keV, approaching the chaos-related unpredictability limit ($sim 100$ keV).
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