If you can do so, get rid of overly negative employees. See if you can transfer them to another department that will provide a more positive environment for them. If this can’t be done, and you can restructure the work to allow this possibility, isolate them so they have as little contact as possible with the rest of your staff.
That will enable you to handle the symptoms of the problem. You still have to get to the cause. To do that, you need to sit down with them. Deal with their gripes if they are valid, and make sure that the other staff members know that you’ve done this. If the complaints aren’t valid, don’t just ignore the issues. Talk to those with grievances and explain the situation. Explain, too, to the staff that the complainers have no reason to whine or gripe. More than likely, most of your employees have found these employees’ continuous complaining as annoying as you have.
But don’t stop there. Meet with all your other workers to determine if they have any gripes about either you or the department. Focus on any real problems that might cause poor morale. Show your entire department that you want to keep them happy if you can.
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Sometimes long-term attitudes may be held secretly by staff members. Open meetings enable them to express their feelings. Probe to find out why such attitudes exist. It may be based on past bad experiences with the company, circumstances that no longer exist. If the cause of negativity stems from a "them versus us" thinking, you will have a much more difficult time changing their feelings. Change won’t happen overnight, but demonstrating common interests and concerns can help overcome the attitude.