Its quite simple .
Login in to your Facebook account .
Go to your Group .
There click on Edit members on the right side below the Group Picture .
You will see a screen Given below .
Now make the person admin of the page to whom you want to give Ownership of a Group .
Now click on the Administrators Tab on the same page above .
You will see such window
From there remove yourself from the group by clicking on the cross sign in the right side and confirm your removal .
You are done .