Worldwide long-period observations of five deep-focus earthquakes from the Tonga-Fiji region have been studied. Observed amplitude ratios SKS/SKKS and difference travel times of SKS and SKKS have been compared with theoretical values for conventional core models. The correction of observed discrepancies leads to a new model of the outer core with a zone of increased velocities around 3750-km depth. In spite of extensive search for other, significantly different models explaining the observations, none has been found. Our model implies pronounced chemical inhomogeneity of the outer core.