A medium jump (or “hyper hop”, “mid-jump”, etc.) is a kind of jump characteristic of the King of Fighters series. It is a mix between the small jump and the big jump.
It is performed by inputting a downward direction (, , or ) for an instant, then quickly inputting the desired jump direction (, , or ), also for an instant only. In KOF, you may also tap the jump direction during a dash.
The medium jump is an extremely fast, sharp jump, useful for quickly approaching the opponent.