The classical detective story always ends with the dénouement, the moment when the central mystery is finally unraveled – and "The Murders in the Rue Morgue" is no exception. The last eight paragraphs of the story give themselves over to a nameless sailor, lured to Dupin's home by an advertisement in a local newspaper for a found orangutan (yes, the ape). By the way, the story uses an old-fashioned spelling for our woodland friend that we will try to preserve: "Ourang-Outang."
(Spoiler alert!) It's at this point that we discover that the hideous strength required to kill the victims (Madame L'Espanaye and her daughter) seems inhuman because the culprit isn't human. Here's the story: an escaped ape stumbles into the apartment of the two victims through an open window, tries to play with them, and then gets angry when the scared women struggle to get away. The sailor chasing his ape comes upon this gristly scene, is unable to do anything to save the ladies, and doesn't want to come forward to tell his story for fear of prosecution for murders he didn't commit.
Having told Dupin and the narrator this story, the sailor goes on to catch his lost ape and sell it to the local zoo for lots of money. Dupin and his buddies go to the police and, based on this evidence, get Le Bon, the original suspect, released.
What's key about this ending isn't just whodunit but who solved it: detective work is still new in the world and entirely new in literature (see our "In a Nutshell" for more on this), so Dupin's easy superiority has to be established. We have to know that his way of looking at the world – and that this piece of fiction – is unique.
So we get the last two paragraphs of the story, in which Dupin laughs at the conventional Prefect of Police (i.e., the chief of police). This guy is a "functionary," – a desk-jockey, a pencil-pusher – he doesn't know what it's like outside of the office. And the Prefect doesn't approve of Dupin butting in where he doesn't belong.
But Dupin's all genius-y and superior, and just says, "Let him discourse; it will ease his conscience" (123). In other words, let the Prefect talk, he made a mistake, and feels bad about imprisoning an innocent man. The Prefect has "cunning" and "ingenuity," but what Dupin has is the ability to think outside the box. He knows, as both Star Trek's Spock and Arthur Conan Doyle's Sherlock Holmes say so much later, that once you have eliminated the impossible, whatever remains, however improbable, must be the truth. In other words, Dupin has the imagination to speculate, while the Prefect (along with all ordinary policeman and bureaucrats) remains stuck in his own conventional ways of thinking.
The final line of the story is a quote from 18th century French philosopher Jean Jacques Rousseau's novel La Nouvelle Heloise (a.k.a. The New Eloise). Dupin claims that he admires the Prefect for his ability "de nier ce qui est, et d'expliquer ce qui n'est pas." If you get past the French, this is cold. Dupin likes the way that the Prefect can "deny that which is, and explain that which is not."