High-resolution LEED (low-energy electron diffraction) data of Cu(001) reveal an uniaxial in-plane lattice reconstruction by 1%. One-dimensional nanogrooves induced by ion bombardment involve the creation of steps that enable this reconstruction. This is the first verification of van der Merwe's prediction of step facilitated reconstruction. We confirm the predicted dependence on step orientation: <100> steps allow stress-relief and <110> steps do not, consistent with the known elastic anisotropy. Similar behavior is predicted for other nonreconstructed (001) surfaces of 3d and 4d metals.