An acknowledged minor classic from 1961. Only problem is that I didn't like it very much. As always, your mileage may vary.
It's (yet another) story of a sympathetic professional killer; what is it with moviemakers' fascination with these folks? The hitman here is Frank Bono, played by Allen Baron (who also directed and wrote the screenplay). He's in New York City with a mission to bump off a minor gangster.
Bono is the kind of guy who plans his jobs meticulously. He needs to get a silenced gun from a repulsive dealer. But winds up getting a revolver, which, as any gun nut will tell you, can't be silenced. He stalks his prey, looking for his most unguarded moment, but forgets to find a safe escape route. During the course of the movie he accidentally meets an old friend, and is drawn into his social circle; this makes Bono suddenly yearn for female companionship. As it turns out, that wish is completely unrealistic.
It's self-conciously arty in spots, most noticeable in a Village nightclub scene where a beat group performs jazz with a pretentious guy playing the conga and (sort of) singing. There is also a third-person narrator (uncredited, then-blacklisted Lionel Stander); it's grating tough-guy prose, written by (pseudonymous, also then-blacklisted) Waldo Salt.
It's short, obviously made on a shoestring budget. But it seems much, much longer, because there are endless scenes of Bono walking around, looking moody. Zzzzz.