Increasing evidence has suggested that formation and propagation of misfolded aggregates of 42-residue human amyloid β (Aβ(1-42)), rather than of the more abundant Aβ(1-40), provokes the Alzheimer's disease cascade. However, structural details of misfolded Aβ(1-42) have remained elusive. Here we present the atomic model of an Aβ(1-42) amyloid fibril, from solid-state NMR (ssNMR) data. It displays triple parallel-β-sheet segments that differ from reported structures of Aβ(1-40) fibrils. Remarkably, Aβ(1-40) is incompatible with the triple-β-motif, because seeding with Aβ(1-42) fibrils does not promote conversion of monomeric Aβ(1-40) into fibrils via cross-replication. ssNMR experiments suggest that C-terminal Ala42, absent in Aβ(1-40), forms a salt bridge with Lys28 to create a self-recognition molecular switch that excludes Aβ(1-40). The results provide insight into the Aβ(1-42)-selective self-replicating amyloid-propagation machinery in early-stage Alzheimer's disease.