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Upgrading from an existing JIRA configuration that uses the JIRA 4 - 5.1 plugin to use the JIRA plugin (which supports JIRA 5.2 and above) is easy. Provided that you are using JIRA 5.2 or above, you can simply click on the "Upgrade" button on the Edit External System.
This change is reversible. After upgrading, if you decide to move back to the JIRA 4 - 5.1 plugin, you can simply click on the "Downgrade" button:
All of your project links will automatically be upgraded to use the JIRA plugin.