The saccadic eye movement system provides an excellent model for investigating basic cognitive processes and flexible control over behaviour. While the mechanism of pro-saccades (PS) is well known, in the case of the anti-saccade task (AS) it is still not clear which brain regions play a role in the inhibition of reflexive saccade to the target, nor what is the exact mechanism of vector inversion (i.e. orienting in the opposite direction). Independent component analysis (ICA) is one of the methods being used to establish temporally coherent brain regions, i.e. neural networks related to the task. In the present study ICA was applied to fMRI data from PS and AS experiments. The study revealed separate networks responsible for saccade generation into the desired direction, the inhibition of automatic responses, as well as vector inversion. The first function is accomplished by the eye fields network. The inhibition of automatic responses is associated with the executive control network. Vector inversion seems to be accomplished by the network comprising a large set of areas, including intraparietal sulcus, precuneus/posterior cingulate cortices, retrosplenial and parahippocampal. Those regions are associated with the parieto-medial temporal pathway, so far linked only to navigation. These results provide a new insight into understanding of the processes of the inhibition and vector inversion.