Dear Sl-Somani,
The information provided in your post is too inadequate to give any solution. Please confirm what exactly happened in the chronological sequence. Who was dismissed, when was dismissed, was he/she issued with any show-cause notice before dismissal, whether or not any enquiry was conducted before the dismissal?
If the private bank has dismissed an employee, then it could be because of financial irregularity. Generally, the banks do not take such an extreme measure unless they have material evidence at hand. Nevertheless, when you provide us with all the details of the incident, then we will apply our logic and decide whether or not the dismissal was unfair.
Thanks,
Dinesh Divekar