This paper investigates the spatial organization of nonlinear interactions between different brain regions in healthy human subjects. This is achieved by studying the topography of nonlinear interdependence in multichannel EEG data, acquired from 40 healthy human subjects at rest. An algorithm for the detection and quantification of nonlinear interdependence is applied to four pairs of bipolar electrode derivations to detect posterior and anterior interhemispheric and left and right intrahemispheric interdependences. Multivariate surrogate data sets are constructed to control for linear coherence and finite sample size. Nonlinear interdependence is shown to occur in a small but statistically robust number of epochs. The occurrence of nonlinear interdependence in any region is correlated with the concurrent presence of nonlinear interdependence in other regions at high levels of significance. The strength, direction and topography of the interdependences are also correlated. For example, posterior interhemispheric interdependence from right-to-left is strongly correlated with right intrahemispheric interdependence from back-to-front. There is a subtle change in these correlations when subjects open their eyes. These results suggest that nonlinear interdependence in the human brain has a specific topographic organization which reflects simple cognitive changes. It sometimes occurs as an isolated phenomenon between two brain regions, but often involves concurrent interdependences between multiple brain regions.