In this report we show that the observed inter-neuronal correlation reflects a superposition of correlations associated with the intrinsic correlation between neurons, and correlations associated with variability in the stimuli presented to, or the actions performed by, the subject. We argue that the effects of either stimulus or action variability on the observed correlation, though generally ignored, can be substantial. Specifically, we demonstrate how observed correlations are effected by trial to trial variability in either stimulus or action. In addition, assuming that all relevant stimuli and actions are known, we outline a method for eliminating their effects on the observed correlation. It is also shown that tuning of correlations to a stimulus or an action might be a direct consequence of variability in that stimulus or action, even in the absence of any modulation of direct inter-neuronal interaction. The effects of stimulus and action variability should therefore be carefully considered when designing and interpreting experiments involving multi-neuronal recordings.