  The surface reconstruction of SrTiO$_3$(110) is studied with scanning
tunneling microscopy and density functional theory (DFT) calculations. The
reversible phase transition between (4$\times$1) and (5$\times$1) is controlled
by adjusting the surface metal concentration [Sr] or [Ti]. Resolving the atomic
structures of the surface, DFT calculations verify that the phase stability
changes upon the chemical potential of Sr or Ti. Particularly, the density of
oxygen vacancies is low on the thermodynamically stabilized SrTiO$_3$(110)
surface.
