Structural changes in epitaxial La0.84Sr0.16MnO3-delta (LSMO) (001)/SrTiO3(001) thin films are studied using x-ray scattering during thermal annealing. As oxygen atoms are incorporated during annealing ex situ in air, the unit-cell volume contracts, which is attributed to the increased ratio of Mn4+ ions as indicated by enhanced saturation magnetization and ferromagnetic transition temperature. The unit-cell contraction occurs rather abruptly, suggesting that a structural phase transition happens during annealing. A 200-Angstrom-thick film remains almost fully strained even after annealing. In this case, a fourfold structural modulation is observed which accommodates the augmented lattice strain energy.