On the other hand, the voyager may also feel that he possesses supernormal powers of perception and movement, that he can perform miracles, extraordinary feats of bodily control, etc …
-- Timothy Leary, Ralph Metzner, Richard Alpert, The Psychedelic Experience
The limbs twitched, the eyes gleamed, the blood-pressure appeared heightened, and there was a supernormal pinkness in the epidermis of the cheek.
-- P. G. Wodehouse, Summer Lightning
Supernormal was first used in the 1860s. The prefix super- has a number of common senses. In this case, it is used in the sense of "an individual, thing, or property that exceeds customary norms or levels" as in superstar.