Method for constructing large floating units, like drilling rigs, comprising forming upright support columns on floating units and floating the floating units to a mounting site; ballasting the floating units with the upright columns thereon to temporarily submerge the units until only the tops of the columns are exposed; forming a rig carrying platform supported on floatable parallelepipedic bodies and floating the platform and bodies to the columns until the platform is over the submerged columns; deballasting the columns and floating units to cause the columns to rise into engagement with the platform and joining the columns and platform.