Functional connectivity examines temporal statistical dependencies among distant brain regions by means of seed-based analysis or independent component analysis (ICA). Spatial ICA also makes it possible to investigate functional connectivity at the network level, termed functional network connectivity (FNC). The dynamics of each network (ICA component) which may consist of several remote regions is described by the ICA time-course of that network; hence FNC studies statistical dependencies among ICA time-courses. In this paper, we compare comprehensively FNC in the resting state and during performance of an auditory oddball task in 28 healthy subject and 28 schizophrenic patients on relevant (non-artifactual) brain networks. The results show abnormalities both in the resting state and during the task but also the difference of the two states. Moreover, our results suggest that using data both in the resting-state and during the task can better separate the two groups. It is demonstrated that for three pairs of networks, the FNC of the healthy controls resides within a confined region of the correlation space whereas patients behave more sparsely. This can be used to discriminate the two groups based on partitioning the correlation space during the resting state and the task data.