Functional neuroimaging reveals both increases (task-positive) and decreases (task-negative) in neural activation with many tasks. Many studies show a temporal relationship between task positive and task negative networks that is important for efficient cognitive functioning. Here we provide evidence for a spatial relationship between task positive and negative networks. There are strong spatial similarities between many reported task negative brain networks, termed the default mode network, which is typically assumed to be a spatially fixed network. However, this is not the case. The spatial structure of the DMN varies depending on what specific task is being performed. We test whether there is a fundamental spatial relationship between task positive and negative networks. Specifically, we hypothesize that the distance between task positive and negative voxels is consistent despite different spatial patterns of activation and deactivation evoked by different cognitive tasks. We show significantly reduced variability in the distance between within-condition task positive and task negative voxels than across-condition distances for four different sensory, motor and cognitive tasks--implying that deactivation patterns are spatially dependent on activation patterns (and vice versa), and that both are modulated by specific task demands. We also show a similar relationship between positively and negatively correlated networks from a third 'rest' dataset, in the absence of a specific task. We propose that this spatial relationship may be the macroscopic analogue of microscopic neuronal organization reported in sensory cortical systems, and that this organization may reflect homeostatic plasticity necessary for efficient brain function.