This paper describes a new method, single-link cluster analysis (SLC), to evaluate percursory quiescence for shallow earthquakes in sixteen subduction zones, using data from the ISC catalog. To define quiescent regions, we divided the catalog into time intervals with a durationT, overlapping byT/2. We considered all earthquakes having magnitudes larger than some magnitudeMmin, lying within a specified distance of a great circle which is approximately coincident with the trench near a subduction zone. Within each time interval we connected or ‘linked’ all earthquakes lying within some cutoff distanced of one another. We then projected all these links onto the great circle, and defined a region to be quiescent if it was not covered by the projection of any links. For this study,T was two years,Mmin wasmb=4.9, and we variedd from 100 to 400 km. We defined an earthquake as ‘following quiescence’ if it occurred within two years following, and within 75 km of a quiescent zone as defined above. The primary conclusion of this study was that earthquakes with surface wave magnitudes 7.2 and greater were about 5–15% more likely to follow quiescence than were the smaller background earthquakes withmb>-4.9. A chi-squared analysis shows that this result is significant at the 99% level. In contrast, earthquakes with surface wave magnitude of 6.7 to 7.1 were no more likely to follow quiescence than were background earthquakes. Of sixteen individual regions, Central America, Japan, and Peru-Chile were the only regions where large earthquakes were more likely to occur following quiescence than were background earthquakes. For a cutoff link length of 300 km, only in Central America was the difference between large earthquakes and background earthquakes significant at the 95% level of significance. For a cutoff link length of 250 km, the significance level exceeded 95% only in Japan. The SLC method is an objective, quantitative method for evaluating large data catalogs, or for monitoring quiescence in regions where quiescence is conjectured to precede large earthquakes.