The Royal Navy frigate, HMS Cyane, is one of only two wooden vessels known to have been built by John Bass, the Lympstone shipbuilder (the other being the Royal Navy gunbrig HMS Urgent).
There was an earlier Cyane because there is a reference on the WWW to one being built for the Royal Navy in 1796 at Frinsbury (presumably near Rochester in Kent):
This Cyane saw service in the West Indies until "...she was captured on 12 May 1805 by the French HORTENSE and HERMIONE and recaptured off Torbago on 5 October 1805 by Capt. George TOBIN in PRINCESS CHARLOTTE,38, and renamed CERF because a new 22-gun CYANE was in service".
The above information applies to the earlier HMS Cyane.
It appears that the Cyane built by Bass at Topsham in 1806 was originally named Columbine: It is described as a sixth rate (32 guns or less), so was one of the Royal Navy's smallest class of warship. Being a frigate, it had three masts with square sails. There appears to be some doubt about whether the Cyane was built in Topsham or Lympstone because the well-respected authority, Michael Oppenheim, in his book "The Maritime History of Devon" (Exeter University 1968 although written in 1908) states that the Cyane was built in Lympstone.
This is pure conjecture but 1806, the year the Cyane was built, was the year that the short-lived partnership of John Bass and  John Bishop in Tilney Rising's old yard at the end of The Strand, Topsham was dissolved, so perhaps the ship could have spent time in both yards, e.g. built at Topsham and fitted out at Lympstone.
At http://www.pbenyon.plus.com/Naval_History/Vol_V/P_175.html there is an account of an action  on 24/27 June 1809 near Naples in the Mediterranean involving a Royal Navy ship called the Cyane described as a "22-gun ship". It was commanded by Captain Thomas Staines who lost his left arm in the action. The damage to the ship was so great that "the Cyane was immediately sent to England to be refitted":
There are a considerable number of accounts on the WWW which make reference to the ship HMS Cyane, in connection with her capture, 20 February 1815, along with HMS Levant by the USS Constitution during the War of 1812 (actually just after peace had been agreed because of the slowness of communications at the time!). The Cyane suffered serious damage and 6 dead and 29 wounded before Captain Gordon Falcon surrendered. After her capture, HMS Cyane became the USS Cyane, being broken up sometime after 1835.
Many of the sites repeat the same story, so here are just a few references:
http://www.pbenyon.plus.com/Naval.html
There is a detailed article on Wikipedia about the circa 30 year life of HMS Cyane at : http://en.wikipedia.org/wiki/HMS_Cyane  illustrated with a photograph of a model of the ship, built by Hans Heinz Binder of Vienna, Austria.

 Also this excellent account.

The USS Constitution, also known as "Old Ironside", can be seen today as a floating exhibit at the Charleston, MA Navy Yard