"on the stern" is correct and can be used in written English.
It is most often used when referring to a boat, as in the sentence, "The captain stood on the stern of the ship, surveying his crew."
There was superficial damage to gilded carvings on one side and a wooden crown on the stern was knocked overboard.
Espingole mounted two single 381 mm torpedo tubes: one between the funnels and the other on the stern.
One was mounted on the stern in a swivel mount, one was mounted submerged in the bow, and one was placed submerged in the hull on either side abreast of the forward gun turret.
All of the 16-inch and 5-inch guns would have been removed, though the number one turret would have remained so that weights added on the stern half of the ship could be balanced.
Without hesitating, I stood on the stern and leaped.
On a platform on the stern sits a helicopter.
Late in the afternoon, I stood beside him on the stern, watching the slick.
Alas, experience is a "lantern on the stern, which shines only on the waves behind us".
His boat was not a canoe, and the object on the stern was no paddle.
She claimed on the Stern show that she and Belafonte had sex five times a day.
From a pole on the stern, the ship flew a Chinese-style red flag.
