Electron diffraction in free-standing liquid-crystal films of N-(4-n-butoxybenzylidene)-4-n-octylaniline between 3 and 12 molecular layers thick reveals the unusual occurrence of the smectic-A' phase, a highly correlated isotropic liquid, on the surface of smectic-A films. The surface smectic-A-smectic-A' transition is found to be first order. Surprisingly, the temperature range of the subsequent surface hexatic-B phase is reduced with decreasing film thickness.