Strain relaxation is very important for the fabrication of smooth heteroepitaxial films with abrupt interfaces. At fcc(111) surfaces, strain is very efficiently relieved through the formation of fcc-hcp stackings, which are usually arranged in mesoscopically ordered networks. At fcc(100) surfaces, however, fcc-hcp stacking faults are symmetrically impossible. We report here on a novel mechanism-internal (111) faceting-of strain relief at heterointerfaces with square symmetry. The mechanism has been revealed for thin Cu films on Ni(100) by variable temperature scanning tunneling microscopy. In the first monolayer, monatomic chains of Cu atoms are shifted laterally from the fourfold hollow configuration to the twofold bridge configuration and thereby protrude from the surface layer. The gain in lateral freedom of expansion of the protruding atoms overbalances their lowered binding energy. With each Cu layer added the relaxed stripes grow in width by one atom, forming internal {111} interfaces in the Cu film. In this mode the film grows layerwise up to about 20 monolayers where bulk dislocations are formed through merging stripes.