REMs (Reinforceing [sic] Enigmatic Matrix) are Schwarz-modified versions of GEMs. The only one known to exist is used by Midori. It resembled a large green lens worn on the back of a glove granting its user strength near that of a Robed Otome, via nanomachines, before breaking down after a short time. Yohko Helene modified it to last indefinitely until depowered for discardment. This is proven by the infinity symbol which is an inverted number 8 when Midori activated her powers.
In the manga, Arika Yumemiya also uses a REM for a short period of time after the Founder is revived. It is loaned to her by Midori because it allows her to materialize the Sky Blue Sapphire's Robe without confirmation from Mashiro and, more importantly, without the Founder's assistance.