Extraction of relevant features from multitask functional MRI (fMRI) data in order to identify potential biomarkers for disease, is an attractive goal. In this paper, we introduce a novel feature-based framework, which is sensitive and accurate in detecting group differences (e.g. controls vs. patients) by proposing three key ideas. First, we integrate two goal-directed techniques: coefficient-constrained independent component analysis (CC-ICA) and principal component analysis with reference (PCA-R), both of which improve sensitivity to group differences. Secondly, an automated artifact-removal method is developed for selecting components of interest derived from CC-ICA, with an average accuracy of 91%. Finally, we propose a strategy for optimal feature/component selection, aiming to identify optimal group-discriminative brain networks as well as the tasks within which these circuits are engaged. The group-discriminating performance is evaluated on 15 fMRI feature combinations (5 single features and 10 joint features) collected from 28 healthy control subjects and 25 schizophrenia patients. Results show that a feature from a sensorimotor task and a joint feature from a Sternberg working memory (probe) task and an auditory oddball (target) task are the top two feature combinations distinguishing groups. We identified three optimal features that best separate patients from controls, including brain networks consisting of temporal lobe, default mode and occipital lobe circuits, which when grouped together provide improved capability in classifying group membership. The proposed framework provides a general approach for selecting optimal brain networks which may serve as potential biomarkers of several brain diseases and thus has wide applicability in the neuroimaging research community.