Object-centered spatial awareness--awareness of the location, relative to an object, of its parts--plays an important role in many aspects of perception, imagination, and action. One possible basis for this capability is the existence in the brain of neurons with sensory receptive fields or motor action fields that are defined relative to an object-centered frame. In experiments described here, neuronal activity was monitored in the supplementary eye field of macaque monkeys making eye movements to the right or left end of a horizontal bar. Neurons were found to fire differentially as a function of the end of the bar to which an eye movement was made. This is direct evidence for the existence of neurons sensitive to the object-centered direction of movements.