Ion beam assisted deposition (IBAD) allows a biaxial texturing of oxide layers on polycrystalline or amorphous substrates. Even the best layers still contain an in-plane angular spread of about 4°. We report here a method to grow Ir films on top of these oxide layers with a factor of 5 lower misorientation. It is shown that the huge texture improvement involves a massive realignment of the iridium islands and an orientation averaging process. Heteroepitaxial diamond was successfully deposited on the Ir/IBAD-MgO multilayer stacks. The described texture improvement by iridium layers provides a general concept towards single crystal growth on arbitrary substrates.