One of the functions of the cerebral cortex is to increase the selectivity for stimulus features. Finding more about the mechanisms of increased cortical selectivity is important for understanding how the cortex works. Up to now, studies in multiple cortical areas have reported that suppressive mechanisms are involved in feature selectivity. However, the magnitude of the contribution of suppression to tuning selectivity is not yet determined. We use orientation selectivity in macaque primary visual cortex, V1, as an archetypal example of cortical feature selectivity and develop a method to estimate the magnitude of the contribution of suppression to orientation selectivity. The results show that untuned suppression, one form of cortical suppression, decreases the orthogonal-to-preferred response ratio (O/P ratio) of V1 cells from an average of 0.38 to 0.26. Untuned suppression has an especially large effect on orientation selectivity for highly selective cells (O/P < 0.2). Therefore, untuned suppression is crucial for the generation of highly orientation-selective cells in V1 cortex.