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Generally, the trust agreement will have provisions to appoint the initial trustee and will also dictate when and how a successor trustee will be appointed. In most cases it is not necessary to amend the trust agreement to change trustees.
If you want to change trustees in any manner which is not in accordance with the trust agreement as originally adopted then you will have to amend the trust agreement before you can make such a change.
Some caution should be taken to ensure that all the formalities are followed so it may be best to have the attorney that originally formed the trust make any changes that are needed (or at least be consulted before changes are made) .
I hope this helps for the general rules for changing a trustee.