Termination policy if employee's behaviour is negatively effecting business

We have an employee whose performance is not at all good. He is very rude with client and it seems to be effecting business. As a result, management decided to terminate his employment immediately- without any prior warning.
Here, my question is, can we terminate his employment without any warning letter issued and not paying anything or do we need to pay one month salary then terminate employment?
please suggest.

What is his status of employment - a probationer or a confirmed employee? In case of his being a probationer, you can simply discharge him without assigning any specific reason if so provided for in the contract of employment; if he is a confirmed employee, you cannot dispense with his services so simply as you mentioned. You have to take a formal disciplinary action against him on specific charges, conduct a domestic enquiry and following all these only you can terminate his services.

He is a senior resource guy where we have not mentioned any probation at the time joining and reporting manager of him given feedback multiple times about his performance but employee still repeating the same behavior with client.

Better talk to him and explain his professional weakness, in dealing with client. Being a senior resource, suggest him a job rotation, which is inevitable, where job responsibility would be tougher, and suggest him that he would be reporting to a younger generation Manager. Most likely he will opt for resignation.

Hi,
Please document the verbal warnings and file the same in his personal file. In case of no improvement start issuing warning letters asking him to realign his working style and further proceed with termination. But ensure you follow the disciplinary process. The other probability is in case of multiple of warnings he himself might submit resignation.

Hello
You should follow disciplinary Action like , Warning Letter , show cause notice , Conduct inquiry