Simultaneously recorded neurons often exhibit correlations in their spiking activity. Short-term synaptic plasticity (STP) allows synapses to perform critical computational functions in neural circuits. It is critical to understand the properties and mechanisms that generate correlation and the role of STP in these forms of correlation. A nonmonotonic relationship between the output correlation and the negative feedback strength is found in the present paper. By numerical simulations, we also find that when we add STP to the feedback loop the tendency of the changes of the output correlation corresponds to the trajectory of the nonmonotonic curve.