The evaluation of the individual “fingerprint” of a human functional connectome (FC) is becoming a promising avenue for neuroscientific research, due to its enormous potential inherent to drawing single subject inferences from functional connectivity profiles. Here we show that the individual fingerprint of a human functional connectome can be maximized from a reconstruction procedure based on group-wise decomposition in a finite number of brain connectivity modes. We use data from the Human Connectome Project to demonstrate that the optimal reconstruction of the individual FCs through connectivity eigenmodes maximizes subject identifiability across resting-state and all seven tasks evaluated. The identifiability of the optimally reconstructed individual connectivity profiles increases both at the global and edgewise level, also when the reconstruction is imposed on additional functional data of the subjects. Furthermore, reconstructed FC data provide more robust associations with task-behavioral measurements. Finally, we extend this approach to also map the most task-sensitive functional connections. Results show that is possible to maximize individual fingerprinting in the functional connectivity domain regardless of the task, a crucial next step in the area of brain connectivity towards individualized connectomics.