We have studied the dimer of amyloid beta peptide Aβ of 40 residues by means of all-atom replica exchange molecular dynamics. The Aβ-dimers have been found to be the smallest toxic species in Alzheimer's disease, but their inherent flexibilities have precluded structural characterization by experimental methods. Though the 24-μs-scale simulation reveals a mean secondary structure of 18% β-strand and 10% α helix, we find transient configurations with an unstructured N-terminus and multiple β-hairpins spanning residues 17-21 and 30-36, but the antiparallel and perpendicular peptide orientations are preferred over the parallel organization. Short-lived conformational states also consist of all α topologies, and one compact peptide with β-sheet structure stabilized by a rather extended peptide with α-helical content. Overall, this first all-atom study provides insights into the equilibrium structure of the Aβ1-40 dimer in aqueous solution, opening a new avenue for a comprehensive understanding of the impact of pathogenic and protective mutations in early-stage Alzheimer's disease on a molecular level.