How do you handle this type of person?

I have a coworker who gossips around saying that I stab her in the back. The real issue is she always makes mistakes and I have to correct it. I have to correct these mistakes because it is my job. I emailed her, but she refused to admit her mistakes or would say something like she doesn't know the procedure; she doesn't know what to do. If I tried to explain to her, she would directly refuse me by saying: I am busy; I have priorities.
Now the management in the dept has changed. I hate to see they think that I am not getting along with this woman. Yes, we are not getting along; but it is all her faults, all her mistakes. she is a black, HR are all black too; so I think the new management doesn't want to get involved in this.
The previous management know about the issue but they just kept silent until they are gone.
Type the above passage during the lunch break; sorry, no Chinese software.
Is there any better way to get the job done?