How do I get rid of a coworker

That my boss refuses to fire. She's been a problem every since she got hired a year ago. She's unprofessional, immature, crazy, and incredibly stupid. I'm her supervisor but I don't have the authority to fire her. The entire office and multiple patients have complained about her, our boss does nothing but talks to her. She claims to be looking for a replacement but it's a weak effort.

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Gusman · 61-69, M

Move her to a department that she will not enjoy or will stuff up continually?
Maybe she will quit

Lilliesandlight · 41-45, F

@Gusman we keep hoping she will, she's made no secret that she hates her job. There's no where for her to go, it's a small practice. She's refusing to quit because she knows everyone wants her too.

Gusman · 61-69, M

@Lilliesandlight Then the boss needs to step up.
If she is the reason for the discontent in the ranks then she must go.
The boss knows this but has little courage.
Is there a spokesperson in your ranks who can talk with the boss?

Lilliesandlight · 41-45, F

@Gusman yes I agree. She's written her up for yelling at the doctor, threatened to fire her if she acts up again. Of course she has and she's still not fired. I've reported every incident of her rudeness and incompetence to my boss. She's made a weak attempt at finding a replacement. We are about to lose our nurse who's been there for 17 yrs, a hard worker and who is professional, over this BS.