Ms Byrne (35) from Dunboyne, Co Meath, was 38 weeks pregnant with twin boys when she died following a fall at Howth summit after going missing from her home.
Her husband Terry Byrne last spoke to her the previous day -- on March 7 -- when she told him she was going to the supermarket.
"At the end of the call, I told her to phone any time if there was anything," he told the coroner's court. "We told each other that we loved each other and she said 'I'll see ya later'."
However, she failed to turn up to collect their son from school later that day and a nationwide search began.
Rescue workers recovered her body on the rocks at Howth in the early hours of March 8.
Coroner Dr Brian Farrell said suicide could not be proved beyond reasonable doubt and recorded an open verdict.
Less than a week before her death, Mrs Byrne and her husband Terry attended consultant psychiatrist Dr John Sheehan and told him that she was "preoccupied with having a daughter" and was "devastated" when she discovered she was carrying twin boys.
Master of the Rotunda Dr Sam Coulter Smith, who did not treat Mrs Byrne personally, said on RTE's Morning Ireland that although a history of depression was recorded for previous pregnancies, the psychiatric team's notes were kept separate in a bid to maintain confidentiality.
"It is important to note that the coroner gave an open verdict in this case. It is also important to note that there weren't any care issues involved in this case," he said.
"It was important not to have a 'knee-jerk reaction'," he added.
"What we will do is, we will take on board the comments the coroner made, and the family. I'm going to be sitting down later this week with my colleagues from the psychiatric subspecialty with which we work with and we will review the care procedure."