If you no longer wish to share a joint current account with a person, you can remove your name from the account. Once you aren't named on the account, you will no longer have access to the assets in it. You will also not be entitled to the records of financial transactions that take place with that account. Not every bank will allow you to remove a name from an account. In that case, the only way to remove your name is to close the account entirely.
Visit your bank. Bring any documentation you have for the joint account. Also bring your identification.
Ask if the bank can remove your name from the joint account. Some banks will not do this, but some will. The bank may require that the other person on the account be present.
Sign paperwork relinquishing your right to the account. Turn in any checks or cards associated with the account.
Withdraw all funds from the account and close it entirely if the bank will not remove your name from the joint account.
Create a new bank account for yourself. The other person on the joint account can deposit funds into a new account he creates as well.