No. If you have already completed the FAFSA for one student, you do not need to complete a new FAFSA for a second student. You can simply add the second student to your existing FAFSA. To do this, log in to your FAFSA account and click on the "Add Student" link. You will then need to provide the second student's name, Social Security number, and other relevant information.
Once you have added the second student to your FAFSA, you will be able to submit the form and the information will be sent to the colleges and universities that both students are applying to.