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Background: Functional connectivity quantifies the statistical dependencies between the activity of brain regions, measured using neuroimaging data such as functional magnetic resonance imaging (fMRI) blood-oxygenation-level dependent time series. The network representation of functional connectivity, called a functional connectome (FC), has been shown to contain an individual fingerprint allowing participants identification across consecutive testing sessions. Recently, researchers have focused on the extraction of these fingerprints, with potential applications in personalized medicine. Materials and Methods: In this study, we show that a mathematical operation denominated degree-normalization can improve the extraction of FC fingerprints. Degree-normalization has the effect of reducing the excessive influence of strongly connected brain areas in the whole-brain network. We adopt the differential identifiability framework and apply it to both original and degree-normalized FCs of 409 individuals from the Human Connectome Project, in resting-state and 7 fMRI tasks. Results: Our results indicate that degree-normalization systematically improves three fingerprinting metrics, namely differential identifiability, identification rate, and matching rate. Moreover, the results related to the matching rate metric suggest that individual fingerprints are embedded in a low-dimensional space. Discussion: The results suggest that low-dimensional functional fingerprints lie in part in weakly connected sub-networks of the brain and that degree-normalization helps uncovering them. This work introduces a simple mathematical operation that could lead to significant improvements in future FC fingerprinting studies.