Does Undead Fortitude work if you have only 1 HP?

Undead Fortitude. If damage reduces the zombie to 0 hit points, it must make a Constitution saving throw with a DC of 5+the damage taken, unless the damage is radiant or from a critical hit. On a success, the zombie drops to 1 hit point instead.

If a zombie has 1 HP (usually from activating Undead Fortitude), can it use Undead Fortitude again?

The description states ‘drop to 1 hit point instead’, which arguably 1 HP cannot drop to 1 HP. You must have more than 1 HP to drop to 1 HP. In other video games I’ve played, a feature like this usually also requires more than 1 HP to activate (to prevent unkillable player or enemy) – to give insight on usual game design perspective.