It is generally believed that the resolution in digital holography is limited by the size of the captured holographic record. Here, we present a method to circumvent this limit by self-extrapolating experimental holograms beyond the area that is actually captured. This is done by first padding the surroundings of the hologram and then conducting an iterative reconstruction procedure. The wavefront beyond the experimentally detected area is thus retrieved and the hologram reconstruction shows enhanced resolution. To demonstrate the power of this concept, we apply it to simulated as well as experimental holograms.