Abstract: A method of building multistory structures having poured concrete slabs. Vertical structural columns and other nonstructural members penetrating the finished floor slabs are terminated at each floor below the level of the finished slab. The slab is then poured, covering the terminated structural and nonstructural members with a thin layer of concrete, and leaving an upper slab surface unencumbered by upward projections. The entire slab is then screeded by a screeding machine in one pass. In an alternative embodiment, the screeding machine makes more than one pass, but the upper surface is still unobstructed. The thin layer of concrete is readily discerned by coloration differences, and is chipped away and removed. All penetrating members are then extended. The process is repeated until all slabs are completed. The novel method is usable with both steel and poured concrete columns.