We examined daytime movements of a herd of African elephants (Loxodonta africana) at 10-min, 15-min, and 20-min intervals in Pongola Game Reserve, South Africa. This group tended to proceed in a consistent direction during consecutive movements, especially during long moves. Serial movement lengths and serial movement angles were autocorrelated at 10-min and 15-min intervals but not at 20-min intervals, indicating that 20-min intervals may be a suitable temporal scale to avoid oversampling. Herd movements followed a Lévy-modulated correlated random walk. In addition, looping movements were detected. Spatial scale of the loops averaged about 1 km. Movement strategies that include both Lévy walks and correlated random walks are thought to optimize foraging.