Making a process unique means several actions in the following sequence:

• Clone the current process/ System suggests default name for a new process: %original_process_name (%record_name%)
• Set "yes" value to "The process will be used for a single record?" property (that will prevent from starting this process on other record again)
• Activates cloned process
• Clone current process instance with all steps active and completed as they were in original instance

To make process unique select the process instance and click "Make Unique" button, then change suggested process name (if needed) and confirm.