The behavior of the surface barrier that forms at the metal-vacuum interface is important for several fields of surface science. Within the density functional theory framework, this surface barrier has two nontrivial components: exchange and correlation. Exact results are provided for the exchange component, for a jellium metal-vacuum interface, in a slab geometry. The Kohn-Sham exact-exchange potential V(x)(z) has been generated by using the optimized effective potential method, through an accurate numerical solution, imposing the correct boundary condition. It has been proved analytically, and confirmed numerically, that V(x)(z--> infinity) --> -e(2)/z; this conclusion is not affected by the inclusion of correlation effects. Also, the exact-exchange potential develops a shoulderlike structure close to the interface, on the vacuum side. The issue of the classical image potential is discussed.