The Psywave desync glitch is a natural glitch in Pokémon Red, Blue, and Yellow.
When Psywave is used by the player its damage will range between 1 and x (where x=attacker's current level + floor[attacker's current level/2). However, when Psywave is used by the foe its damage may also range between 0 and x.
It is possible to desynchronize a link battle if one of the players deals 0 HP damage, because according to player 1's side they would have dealt 1 HP but 0 HP on player 2's side.
There is a higher chance for this glitch to occur lower level Psywave user (1/3 for level 2 but 1/150 for level 100).