The easy way is simply to close the account and open a new one. If it is a CD or other account which cannot be closed without a penalty simply do not renew it and transfer the funds to another account at maturity. This is a common occurrence. Banks frequently insist on closing an account as opposed to changing account holders.
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Closing account is probably the easiest solution. However, I would consider doing a new trust if the old trust no longer meets your needs or estate planning goals. A Living Trust enables you to appoint a Trustee to handle your finances for you in the event you are disabled without having to go to court to have a Conservator or Guardian appointed. It also allows you to transfer your assets at death to your beneficiaries in a private manner without a court probate. I would recommend that you speak to an estate planning attorney.
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It sounds like something is missing from your question. That said, the simplest way would be to just withdraw all the money and take it to a different bank.
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