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We investigated the lattice strain in epitaxially grown -oriented Co-Pd superlattices on MgO single-crystal substrates using high-resolution transmission electron microscopy. We observed the elastic deformation of the lattice arrangement from cubic to tetragonal by lateral coherency strain and the intermixed Co-Pd layer with a thickness of 0.5 nm. The tetragonal deformation in the Co-Pd intermixed layer caused by stretching strain from the Pd layer induces high negative magneto-elastic energy via positive magnetostriction, resulting in a high negative contribution to perpendicular magnetic anisotropy energy. In a Co layer less than 0.5-nm thick, the perpendicular anisotropy is enhanced owing to the relaxation of the lattice strain by taking a sinusoidal composition distribution in the modulated direction. We found that post-deposition annealing to -oriented Co-Pd superlattices can improve the perpendicular magnetic anisotropy owing to the effect of interfacial mixing which can relax the coherency strain.