We report our search for doublets in the South Sandwich Islands (SSI) region among 906 earthquakes from January 1982 to December 1998. Event pairs with source separation less than 40 km, which was calculated using PDE locations, were checked using vertical component short period and broadband digital records. Cross correlation coefficients of P (or PKP) waveforms were computed for similarity comparison. Whole waveforms of those event pairs with correlation coefficients larger than 0.8 were checked by eye. By this process, 17 doublets were found, some of which form multiplets. However, only one doublet event pair (14 August 1995 and 28 March 1987) has clear PKP(DF) phases on both records at College, Alaska (COL). The PKP(DF) travel time change measured by cross correlation is a decrease by 0.15 s, with standard deviation 0.02 s, over a time period of about 8 years. This result strongly supports differential rotation of the Earth's inner core relative to the mantle and the crust. The estimated rotation rate ranges from 0.4¿ to 1¿ per year eastward. The special case of a locked inner core can then be ruled out. We also checked the precision of PDE and ISC locations using the 17 doublets. Results show that both catalogs have relatively high location precision. Standard deviations in latitude, longitude and depth are less than 4 km, 6 km, and 10 km respectively, supporting prior claims of detection of inner core rotation <Song and Richards, 1996>.