A rhesus monkey was trained to move its arm in a direction that was perpendicular to and counterclockwise from the direction of a target light that changed in position from trial to trial. Solution of this problem was hypothesized to involve the creation and mental rotation of an imagined movement vector from the direction of the light to the direction of the movement. This hypothesis was tested directly by recording the activity of cells in the motor cortex during performance of the task and computing the neuronal population vector in successive time intervals during the reaction time. The population vector rotated gradually counterclockwise from the direction of the light to the direction of the movement at an average rate of 732 degrees per second. These results provide direct, neural evidence for the mental rotation hypothesis and indicate that the neuronal population vector is a useful tool for ``reading out'' and identifying cognitive operations of neuronal ensembles.