Can you be fired from a job because another employee started a false rumor?

A friend a of mine was fired from a daycare because a new employee there reported that my friend had hit here child. The three daycare workers that were there all say that the complaint is completly untrue. Is there anything my friend can do about this. This completely false rumor and her being fired will effect her from being able to get a job at any other daycare.Can you be fired from a job because another employee started a false rumor?
I felt sorry for your friend. But if she did not do it, fight for your innocence and rights to clear your name.Can you be fired from a job because another employee started a false rumor?
In this situation, the best thing your friend can do is seek legal advice. You don't say where you are UK, USA etc. but I would imagine that dismissal without evidence of any misconduct would be challengable.
yes is it called employee at will. I suggest she goes to unemployment