Head motion during functional Magnetic Resonance Imaging acquisition can significantly contaminate the neural signal and introduce spurious, distance-dependent changes in signal correlations. This can heavily confound studies of development, aging, and disease. Previous approaches to suppress head motion artifacts have involved sequential regression of nuisance covariates, but this has been shown to reintroduce artifacts. We propose a new motion correction pipeline using an omnibus regression model that avoids this problem by simultaneously regressing out multiple artifacts using the best performing algorithms to estimate each artifact. We quantitatively evaluate its motion artifact suppression performance against sequential regression pipelines using a large heterogeneous dataset (n=151) which includes high-motion subjects and multiple disease phenotypes. The proposed concatenated regression pipeline significantly reduces the association between head motion and functional connectivity while significantly outperforming the traditional sequential regression pipelines in eliminating distance-dependent head motion artifacts.