Temperature dependence of local structure of the CuO 2 plane has been studied by in plane polarized (E//ab) Cu K-edge extended X-ray absorption fine structure (EXAFS) experiments on an under-doped single crystal of superconducting La1.87Sr0.13CuO 4-y system with T c =32 K . The temperature dependence of the Debye–Waller factors for the Cu-O and Cu-La/Sr pairs are determined. We find that the motion of Cu and O atoms in the Cu-O bond is partially correlated at higher temperatures, going over to an uncorrelated motion at lower temperatures. The results are discussed in terms of the local lattice instabilities and stripes as reported in other systems.