Gardaí are also working on the basis that the murders of his wife Clodagh, 39, and three children Liam, 13, Niall, 11 and Ryan, 6, were “planned”.
“An envelope has been found in the house that is believed to be very relevant to the case,” a Garda source confirmed to the Irish Examiner.
The envelope, which was found yesterday, was sent immediately to the Technical Bureau headquarters in Dublin for forensic examination.
Once opened, a working copy of the note is expected to be provided to the investigation team in Ballyjamesduff. It is believed the envelope was marked to be opened only by relatives.
Gardaí also suspect that Mr Hawe, a deputy school principal in Castlerahan National School, planned the murders, which occurred sometime around the early hours of Monday morning.
“He sat down and planned this: it was not blind rage,” said a source.
It is believed that Mr Hawe killed his wife first and then killed his three children, who were asleep at the time.
Ms Hawe, who was a primary school teacher in Oristown NS in Kells, was due to return to work this week, as was her husband.
The family were seen at the local GAA club on Sunday and neighbours in the community said that nothing was amiss.
“It’s just a bombshell. To the outside eye, [there were] absolutely no problems. The house was bought 15 years ago before boom times, probably pretty reasonably, two teacher jobs. You couldn’t see anything in that line,” neighbour and friend Larry McGinn told the Irish Examiner.
He described how Mr Hawe collected money at the gate of the club on Sunday and how he texted him to organise a meeting that was planned for last night.
“If anything went wrong in the community Alan would be on-hand to help out. It’s too sad to even imagine what went on.
“The family were just salt of the earth, a beautiful family and Clodagh was a beautiful person. The kids were involved in church events, community events, and they were just lovely,” Mr McGinn said.
The parents were readers at Mass and the children were all altar servers.
Two scheduled Masses were cancelled yesterday morning and the opening of Mr Hawe’s school was delayed even though it was open for parents, teachers and children to meet in.
Mr McGinn said he was not aware of any health issues Mr Hawe may have had.
“I couldn’t actually imagine asking him if he had any problems. He was always absolutely on the button,” he said.
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