The brain connectome encodes different facets of the brain construct such as function and structure in a network. Noting that a brain network captures the individual signature of a particular subject, it remains a formidable challenge to extract a shared and representative brain signature across a population of brain networks, let alone multi-view brain networks. In this paper, we propose netNorm, a method that can meet this challenge by normalizing a population of multi-view brain networks, where each brain network represents a particular view of the brain, acquired using a neuroimaging technique. While conventional methods integrate the network views equally at a global scale, we propose a selective technique which unfolds the fusion process at a local scale by first selecting for each local pairwise connectivity between two anatomical regions of interest the most representative cross-view feature vector in the population. By combining the selected cross-view feature vectors, we then estimate a population representative tensor. Such multi-view representation captures the most shared traits across all subjects and thereby occupies a centered location compared to all views. In the final step, netNorm non-linearly fuses the frontal views of the estimated representative population tensor into a single network depicting the final brain connectional template. We demonstrate the broad applicability of our method on four connectomic datasets and we show that netNorm (i) produces the most centered and representative connectional brain template (CBT) that consistently captures the unique and distinctive traits of a population of multi-view brain networks, and (ii) identifies disordered brain connections by comparing templates estimated using disordered and healthy brains, respectively, demonstrating the discriminative power of the estimated CBTs. This allows to rapidly and efficiently spot atypical deviations from the normal brain connectome for comparative studies, circumventing the need to use machine learning techniques for discriminative feature identification. (C) 2019 Elsevier B.V. All rights reserved.