December 2009 was one of the quietest (monthly Ap=2) months over the last eight decades. It provided an excellent opportunity to study the day-to-day variability of the F2 layer with the smallest contribution due to geomagnetic activity. With this aim, we analyze hourly values of the F2-layer critical frequency (foF2) recorded at 18 ionosonde stations during the magnetically quietest (Ap=0) days of the month. The foF2 variability is quantified as the relative standard deviation of foF2 about the mean of all the “zero-Ap” days of December 2009. This case study may contribute to a more clear vision of the F2-layer variability caused by sources not linked to geomagnetic activity. In accord with previous studies, we find that there is considerable “zero-Ap” variability of foF2 all over the world. At most locations, foF2 variability is presumably affected by the passage of the solar terminator. The patterns of foF2 variability are different at different stations. Possible causes of the observed diurnal foF2 variability may be related to “meteorological” disturbances transmitted from the lower atmosphere or/and effects of the intrinsic turbulence of the ionosphere-atmosphere system.