The propagation of low-frequency electrostatic surface waves on the interface between a vacuum and an electron-ion quantum plasma is studied in the direction perpendicular to an external static magnetic field which is parallel to the interface. A new dispersion equation is derived by employing both the quantum magneto hydrodynamic and Poisson equations. It is shown that the dispersion equations for forward and backward-going surface waves are different from each other. Published by AIP Publishing.