If the employee admits the charges, there is no need to conduct an inquiry, but you can decide on the punishment and impose it. Before imposing punishment, however, you have to issue a show cause notice and ask the employee to show cause why this punishment should not be imposed on him.
The punishment awarded should equate with the same given in your certified Standing Orders or, in the absence of standing orders, the punishment matrix, as accepted by the employees in general. If you conduct an inquiry on the charges, the process shall be the same as per your current practice, but as far as possible, the employee should be given adequate opportunity to defend the charges leveled against him. He should be given time to present his case in his favor, allowed somebody from the office to assist him in the inquiry, given reasonable adjournments, etc. Above all, in the first sitting itself, he should be given a list of witnesses and documents the company is going to produce against him or in favor of the charges. As far as possible, copies of the evidence should also be given to him for verification and furnishing a reply.
Punishment can be awarded only by the person who is authorized to appoint an employee.
Regards,
Madhu.T.K