A method for installing a TLP based floating object at anchor points. The floating object includes a central body and buoyancy assemblies positioned around the central body in a horizontal plane, with each buoyancy assembly connected to the central body and connectable to one of the anchor points. The method includes: attaching a mooring leg including a mooring line at each anchor point; for each anchor point connecting a pull-down line between the buoyancy assembly and the anchor point; tensioning the pull-down lines so the floating object is lowered to an installation level below an operational level; for each anchor point connecting the mooring leg with the buoyancy assembly in slack mode; and after connecting the mooring lines with the buoyancy assemblies, paying out the pull-down lines so the floating object rises upward from the installation level to the operational level where the mooring legs are tensioned.