If you need to make a department budget permanently inactive, you must close it.
First, go to your Budgets page, and select the one you wish to Close.

Once you open the budget you wish to Close, click the Action (...) button and select Close Budget. Finally, click Yes, Close Budget on the confirmation window. The budget is deleted from your Rho Account, and can no longer be assigned to transactions.

Note: If you need to temporarily make a department budget inactive, you can click the Action (...) button and select Archive Budget.
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