The 15-year-old Tyrone girl disappeared in August 1994 after a night out in Bundoran in Co Donegal.
She was last seen in a car driven by Howard, and her body has never been found.
The coroner described the inquest as an exhaustive interrogation which has re-energised the investigation.
Coroner Brian Sherrard said he hoped “today’s exercise will shed light rather than generate heat”.
After more than a decade of stop, start inquest hearings, members of Arlene’s family were in court on Wednesday to hear the coroner deliver his findings.
He concluded: “Robert Howard, a violent sex offender and the last person to be seen with Arlene on 14 August, was responsible for her death.
“The mechanism of death is unknown.
“The court believes the death occurred in this jurisdiction, but the precise location remains unknown, however the court is confident that her remains were secreted in this jurisdiction as Howard was familiar with the area around Castlederg… and time was limited.
“It is a matter of profound regret that Arlene did not get to live her life.
“I want to reflect on the grave injustice that has been done to the Arkinson family due to the actions of Robert Howard.
“I would like to reflect on the exhaustive manner in which Kathleen in particular has driven this case from the first days after the disappearance right through to today, and that is remarkable, and Arlene herself has been served exceptionally well by her family in the intervening years.”
He debunked several rumours and theories around her disappearance.
He said there was no evidence that she had left Castlederg voluntarily, nor that she had been suicidal, and rumours that she was pregnant were “absolutely false”.
“The court finds Arlene was not pregnant at the time of the disappearance. The fact Howard thought he knew she was sexually active is potentially relevant to this inquest,” he said.
He also dispelled rumours that members of Arlene’s family had been involved in her murder.
The home of her sister, Kathleen, was searched as a result of an anonymous tip off but nothing was ever found.
“Having examined the intelligence, considered the source and other evidence, the court agrees that this presented as a necessary line of enquiry, it could not have been ignored,” he said.
“As a result of this information, the police searched the house… but nothing of evidential value was found.
“There is nothing to substantiate the rumours concerning the family… [but] it would have been impossible for the police not to act.”
The coroner paid tribute to Arlene’s family, who cared for her after the death of her mother in 1990.
He said the commitment of siblings to her welfare was “truly remarkable”.
He added that there was an unwritten story of how the family came together to help and support Arlene, who stayed with various siblings at different times.Howard was charged with her murder but he was acquitted in 2005.
The jury was not told of his history of violent sexual offences and that he had already been convicted of the murder and rape of schoolgirl Hannah Williams in London.
When Arlene disappeared, he was on bail for a series of violent sexual offences against a teenage girl.
He died in prison in 2015, aged 71.
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