The fourth vessel named Amazon to serve in the Royal Navy replaced her predecessor which was wrecked on the French coast in January 1797. As the successor's keel had, in fact, been laid the previous April, it seems likely that the new vessel's name was to have been different but, following the loss of Amazon, the ship already building was chosen to replace her. Built at Woolwich Dockyard to a design by Sir William Rule, she was measured at 1,038 tons and was 150 feet in length with a 39½ foot beam. Carrying a total of 38 guns, her main armament consisted of 28-18pdrs. mounted on her upper deck with additional firepower on her quarterdeck and forecastle.
Eventually launched on 18th May 1799 after what seems an inordinately long time on the stocks for such a relatively small warship, she was commissioned for sea and saw her first action with Nelson at Copenhagen in 1801. One of the five frigates supporting the main battle fleet which attacked the Danish fleet on 2nd April, she was subjected to withering fire from the Trekronen batteries but, under Captain Henry Riou, gave a good account of herself and played no small part in the eventual victory. Thereafter sent to the Mediterranean, she was under orders to watch for a French invasion of Sardinia early in 1804 whilst in January 1805 she engaged and captured a Spanish ship, the Gravina, 140 miles west of Cape St. Vincent. The following year, on 13th March 1806, she was sailing in company with H.M.S. London, 98 guns, south-west of the Canary Islands when they sighted and engaged the French warships Marengo, 74, and Belle-Poule, 40. In a spirited action, London took on the Marengo whilst Amazon dealt with Belle-Poule until both the enemy struck their colours and were taken as prizes.
On 21st January 1810, Amazon captured the French privateer Gìnìral Perignon off Belle Île whilst on 30th July 1811 her boats cut out four enemy chassemarees and burnt five others near Penmarc'h Point, Brittany. Her fighting career ended soon afterwards and, in April 1817, she was broken up at Plymouth, probably the result of post-War cuts in naval expenditure.