Character Analysis
Black Widow
We barely get to know Spade's partner, Miles Archer, before Miles is murdered and Spade has his name removed from the office window (which is just one example of Spade's characteristic coldness). However, we know right away that the murder was suspicious. The detective tells Spade, "His gun was still tucked away on his hip. Hadn't been fired yet. His overcoat was buttoned," leading Spade to realize that Miles was killed by someone he knew.
This sets up one of the movie's red herrings: Iva Archer, the widow in black. Spade is having an affair with Iva, so maybe she killed Miles so she could marry Spade. Iva thinks Spade killed Miles so he could be with Iva. The movie doesn't show us exactly where Spade was when Miles was killed, and Iva was mysteriously missing the night he was murdered, but we're never told where she was. It's all super confusing…and super juicy.
And, like the Falcon, it amounts to nothing. It turns out that Brigid killed Miles. Iva is nothing but a manipulative drama queen, who, "mad, crazy with jealousy" when she sees Spade with Brigid, sends the cops to his door.
Even though Spade couldn't have had that much respect for Miles (he was having an affair with his wife, after all), he does defend him in the end, saying that he has to turn Brigid in to protect the integrity of his partnership with Miles. Iva's storyline is never actually resolved. We can assume Spade never reignites their affair—he'd have to be crazy to. But if you're interested in the Spade/Archer kerfuffle, you should read the book: it explains it in more detail.