Monitoring of aftershock sequences to detect lowering activity, relative to the modeled rate (the relative quiescence), becomes realistic and practical in predicting the enhancement of the likelihood of having a substantially large aftershock, or even another earthquake of similar size or larger. A significant relative quiescence in the aftershock sequence of the 2005 March earthquake of M7.0 off the western coast of Fukuoka, Japan, was reported two weeks before the largest aftershock of M5.8 that also hit the Kyushu District. The relative quiescence was discussed in relation to the stress-shadowing as inhibiting the activity due to probable precursory slips, which are retrospectively speculated in more detail.