In conventional functional near-infrared spectroscopy (fNIRS), systemic physiological fluctuations evoked by a body's motion and psychophysiological changes often contaminate fNIRS signals. We propose a novel method for separating functional and systemic signals based on their hemodynamic differences. Considering their physiological origins, we assumed a negative and positive linear relationship between oxy- and deoxyhemoglobin changes of functional and systemic signals, respectively. Their coefficients are determined by an empirical procedure. The proposed method was compared to conventional and multi-distance NIRS. The results were as follows: (1) Nonfunctional tasks evoked substantial oxyhemoglobin changes, and comparatively smaller deoxyhemoglobin changes, in the same direction by conventional NIRS. The systemic components estimated by the proposed method were similar to the above finding. The estimated functional components were very small. (2) During finger-tapping tasks, laterality in the functional component was more distinctive using our proposed method than that by conventional fNIRS. The systemic component indicated task-evoked changes, regardless of the finger used to perform the task. (3) For all tasks, the functional components were highly coincident with signals estimated by multi-distance NIRS. These results strongly suggest that the functional component obtained by the proposed method originates in the cerebral cortical layer. We believe that the proposed method could improve the reliability of fNIRS measurements without any modification in commercially available instruments.