What you have to do with a Customer who Have a complaint ,if already one of your Colleagues was handling this complaint and fail to deal with him?

We need to re listen the customer carefully to understand his problem in broad scenario there might be miscommunication, misunderstanding which could have cause the mishandling of compliant. Sometime the customer may behave very aggressive but we need to calm down and let him calm down by listening to him in detail, I am sure half of the problem will be resolved only by listening properly and to share his sorrows.

As customer is the pillar of any business form, we must retain the customer at maximum possible limit.

So we must understand the problems of the customer and give him an assurance of consider the same at priority basis.  

First of all come to know the actual need and potential of the customer and try to solve under company's policy. Clear the company's policy and possibilities to demanding customers. Check the potential of customer and make a contingency plan.   '

First, check up whether the complaint is genuine and legitimate. If yes, go out of the way to solve it and satisfy the customer. If not, don't use offensive language, but affirm and clarify the customer, how his complaint is not a valid one.