A new concept in organocatalysis allowing for the construction of cyclobutanes with four contiguous stereocenters with complete diastereo- and enantiomeric control by a formal [2 + 2]-cycloaddition is presented. The concept is based on simultaneous dual activation of α,β-unsaturated aldehydes and nitroolefins by amino- and hydrogen-bonding catalysis, respectively. A new bifunctional squaramide-based aminocatalyst has been designed and synthesized in order to enable such an activation strategy. The potential and scope of the reaction are demonstrated, and computational studies which account for the stereochemical outcome are presented.