The show starred Holywood's Jamie Dornan as serial killer Spector and X-Files FBI agent Gillian Anderson as tough-talking detective Gibson.
Gibson, seconded to Belfast from the Metropolitan Police, is tasked to sniff out serial killer Spector who stalks the city streets for his female prey.
The third series had been criticised for being slow paced but Dornan had promised viewers they could "expect the unexpected".
In the final episode their cat and mouse game came to a violent and unexpected head with Dornan's character attacking the detective leaving her with a bloodied face.
But it was the unsettling climax to the series which has prompted an investigation into the lengthy depiction of suicide through asphyxiation.
A spokesman for Ofcom said "We're investigating whether the depiction of suicide in this programme complied with our rules."
However at the time the BBC defended the finale which left viewers stunned with the graphically-violent end.
It said in a statement: "The Fall is an established drama in its third series, and therefore the protagonist Paul Spector is well known to the audience as a violent and misogynistic serial killer - a character with whom few, if anyone, would identify.
"The scenes are in keeping with previous episodes and the overall narrative of the series. In accordance with editorial guidelines, it transmitted in a post-watershed BBC Two slot and there was a warning prior to broadcast that the drama contains strong and violent scenes that some viewers may find upsetting.
"Production rigorously followed and complied with BBC editorial policy guidelines throughout."
The programme received two complaints over the finale episode and one for the penultimate episode.
Holywood actor Dornan owes a lot to the character and previously said he would play the sinister role until his "dying days" if he could.
He said: "You know, that job changed my life.
"They're like family to me and I'm forever grateful for it to be a part of my life and, you know, I would play that character to my dying days if I had the opportunity."
It's not the first time the programme has drawn criticism as in September series creator Allan Cubitt faced accusations that The Fall glamorised violence against women.
"It was something I had to talk to my daughter about, who has counselled me very well," he said.
"I can't say I've never made any errors or couldn't have done something better or something different, but I know myself and I know these guys and I know what we're all about and that's just an absurd comment."
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