Presumably, when you spoke to her about her tendency to argue, that discussion evolved into an argument as well. By saying that this person is doing a good job, you are probably referring to her technical skills and general ability to complete her work.
However, unless she is working in solitary confinement, she is only doing a good job in part of her job. If her position is one that calls for communication, cooperation, and coordination with other individuals and departments, her performance in these areas must be suffering.
The next time she inappropriately flips into the argumentative mode, let her know that although there may be a time for her to assertively express her opinions, constant arguments are costly, destructive, disruptive, and unacceptable. You should suggest that she develop a specific plan to bring this aspect of her behavior under control. Be sure to let her see the benefits associated with doing so, particularly in terms of the ways that her improved behavior will help her meet her own goals.
If she can develop and commit to a plan to change her behavior, accompanied by your support and feedback whenever she reacts constructively, there is a chance that she will reduce her arguing time. The irony is that by doing so, she will see that she can win more arguments by not arguing at all.
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