Response variability is often positively correlated in pairs of similarly tuned neurons in the visual cortex. Many authors have considered correlated variability to prevent postsynaptic neurons from averaging across large groups of inputs to obtain reliable stimulus estimates. However, a simple average of variability ignores nonlinearities in cortical signal integration. This study shows that feedforward divisive normalization of a neuron's inputs effectively decorrelates their variability. Furthermore, we show that optimal linear estimates of a stimulus parameter that are based on normalized inputs are more accurate than those based on nonnormalized inputs, due partly to reduced correlations, and that these estimates improve with increasing population size up to several thousand neurons. This suggests that neurons may possess a simple mechanism for substantially decorrelating noise in their inputs. Further work is needed to reconcile this conclusion with past evidence that correlated noise impairs visual perception.