We have conducted a series of radiocarbon measurements on decadal samples of dendrochronologically dated wood from both hemispheres, spanning 1000 years (McCormac et al. 1998; Hogg et al. this issue). Using the data presented in Hogg et al., we show that during the period AD 950–1850 the 14C offset between the hemispheres is not constant, but varies periodically (~130 yr periodicity) with amplitudes varying between 1 and 10‰ (i.e. 8–80 yr), with a consequent effect on the ¹⁴C calibration of material from the Southern Hemisphere. A large increase in the offset occurs between AD 1245 and 1355. In this paper, we present a Southern Hemisphere high-precision calibration data set (SHCal02) that comprises measurements from New Zealand, Chile, and South Africa. This data, and a new value of 41 ± 14 yr for correction of the IntCal98 data for the period outside the range given here, is proposed for use in calibrating Southern Hemisphere ¹⁴C dates.