The single-layered half-doped manganite La0.5Sr1.5MnO4 (LSMO), was studied by means of the angle-resolved photoemission spectroscopy (ARPES), scanning tunneling microscopy (STM), and resistivity measurements. STM revealed a smooth reconstruction-free surface; the density of states, extracted from photoemission and tunneling spectroscopy, is in agreement with transport measurements. The derived from ARPES Fermi surface (FS) nesting properties correspond to the known pattern of the charge-orbital ordering (COO), which implies that FS instability is related to the propensity to form a COO state in LSMO.