Your employee needs to understand that she has a job to do, and it is hers, not yours. There is no reason to let her continue to grab your responsibilities just because she goes into a huffy denial mode when you discuss these actions with her.
Your next step is to take a look at her central responsibilities and the extent to which she is successfully carrying them out. She may need to devote more attention to her own work, or perhaps she simply needs more to do. In the latter scenario, you may want to delegate some work to her, but that is your decision only.
Either way, you should provide her with very specific feedback. Clearly describe her actual responsibilities as well as the problems that arise when she tries to carry out your responsibilities without your approval. Show her how her actions undermine communication, coordination, and productivity, and then let her know that this behavior has to stop.
Conclude your discussion by advising her of the possible consequences associated with ignoring you on this matter. If she continues to unilaterally assume your responsibilities, you can unilaterally assume that she is willing to face those consequences.
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