Before considering such a letter, you should explore all possibilities based on reality and truth. Judgment should not be biased. Consult with other employees, assess the work situation, and understand the reasons for uncooperation. With patience, identify the root cause, conduct an investigation, and then seek alternative solutions.
I would be interested in contributing my thoughts to you if you can provide more information about what you saw as unethical or unprofessional in the employee. Like 'neerajdubey' has mentioned, getting to the root of the problem and addressing it will help you take care of future employees who behave in a similar manner.
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