To date, there has been no evidence for the macroscopic structural phase transition to the low temperature tetragonal structure (LTT) with a space group P4 2 /ncm in high-T C cuprate of rare earth-free La 2−x Sr x CuO 4 (LSCO). By investigating Cu-NMR on single crystals, we have found that spatially incoherent LTT structure emerges below 50 K in the sample with x=0.12. This incoherent structure is considered to play a key role for the slight depression of the superconductivity around x=1/8.