Apparently there will soon be a 'King of Limbs: From the Basement' (July 1st), and this was performed there.

Says Spin

Radiohead Debut New Song 'Staircase'

By Kevin O'Donnell on June 21, 2011 9:37 AM

Radiohead may not have that rumored companion album to The King of Limbs in the works, but there's definitely unreleased material from those sessions. The British art-rockers posted a new song, titled "Staircase," on their YouTube account last night; the performance will be featured on their BBC broadcast From the Basement, which premieres July 1. Check out the footage here.

"Staircase," a five-minute, brooding electronic rocker that was left off Limbs, follows the groove-oriented vibe of the disc. Drummer Phil Selway is even joined by a second drummer Clive Deamer — the British jazz session ace who's teamed with trip-hop pioneers like Portishead — and his contributions bring a strong bebop vibe to "Staircase," with virtuosic, tricked-out beats. (Don't be fooled by their physical similarities: "You're not seeing double," Selway wrote. "The doppelganger drummers are myself and Clive Deamer. [He] has long been one of my favorite drummers.") Frontman Thom Yorke, meanwhile, looks to have an absolute blast behind his synth, unleashing his trademark jittery dance moves while delivering the track's icy synth melody.

Supercolider / The Butcher 12"

The King of Limbs Remix 12" series begins July 5th at select independent record stores and will include remixes of “Little By Little” by Caribou and “Lotus Flower” by Jacques Greene