If you are terminated by a bank for no fault of yours, I can understand what you may be going through. Strictly speaking, a termination letter is also a relieving letter. However, producing the same without tact can take you nowhere unless your new employer has fallen in love with you! (And mostly, employers love no one...)
Challenge the Termination
I strongly recommend that you challenge the termination in court. By doing so, you can come clean with your prospective employers and say that you are falsely implicated. Share details and be transparent. It may lend some credence to your claim of false implication.
Make the Dispute Complex
If possible, your dispute should be made out to be rather complex. Figure out which things your bank would hate to have in the public domain or which officers will find it difficult to defend. Make them parties!
Admittedly, courts take time. But if you are smart, you can steer it towards an out-of-court settlement or even separation without stigma if you can scare the bank with the can of worms you can bring in courts/public domain.
Consider Other Options
But frankly, if there is a watertight case against you, please don't try this! Move to a non-banking sector, take a smaller job, or start something on your own for some time. Don't get caught in the past for long. Work on a strategy to move on...
Good wishes!