On the surface of water ice, a quasi-liquid layer (QLL) has been extensively reported at temperatures below its bulk melting point at 273 K. Approaching the bulk melting temperature from below, the thickness of the QLL is known to increase. To elucidate the precise temperature variation of the QLL, and its nature, we investigate the surface melting of hexagonal ice by combining noncontact, surface-specific vibrational sum frequency generation (SFG) spectroscopy and spectra calculated from molecular dynamics simulations. Using SFG, we probe the outermost water layers of distinct single crystalline ice faces at different temperatures. For the basal face, a stepwise, sudden weakening of the hydrogen-bonded structure of the outermost water layers occurs at 257 K. The spectral calculations from the molecular dynamics simulations reproduce the experimental findings; this allows us to interpret our experimental findings in terms of a stepwise change from one to two molten bilayers at the transition temperature.