In our previous study, we investigated the relationship between protein evolution and stability through the random mutational drift of an esterase from hyperthermophilic archaeon Sulfolobus tokodaii. The results revealed that evolvability, which is the appearance frequency of variants with higher activity than the parent protein, correlates with parental stability. This suggests that protein evolution that does not take stability into account does not make sense. Here, we used those data to further evaluate the relationship between activity and stability in random mutations, revealing that the maximum increase in activity due to mutation conflicts with parental stability. That is, many activated variants are produced when parental stability is high, whereas lower stability offers a few excellent variants with much higher activity. Moreover, we used the random mutant library to compute a novel criterion, robustizability (stabilizability), which is the appearance frequency of variants with a higher stability than the parent protein. Robustizability correlates positively with parental activity and negatively with parental stability. The results indicated that the principle of activity-stability trade-off dominates, in even random mutations. We propose its application in protein engineering via directed evolution by stability selection. (C) 2019, The Society for Biotechnology, Japan. All rights reserved.