Nicola Black, 33, was airlifted from Arran to Crosshouse Hospital, Ayrshire, after taking a massive drugs overdose.
But the former teacher, who had a history of mental problems, was not marked as a suicide risk, despite being assessed as of "significant risk" of taking her life.
She was then put in the only room on a ward where window fittings previously flagged up as a ligature risk had, inexplicably, not been removed.
NHS Ayrshire and Arran admitted breaching the Health And Safety At Work Act by failing to communicate to staff that Ms Black was at risk of taking her life, and inadequate record keeping.
Passing sentence at Kilmarnock Sheriff Court, Sheriff Brian Murphy said Ms Black's death was "entirely avoidable" and added: "I regard these failures as serious."
The court heard she had previously been an in-patient Leverndale Hospital, Glasgow, and had gone to Arran, where she sent text messages saying she was going to kill herself before taking an overdose.
She was taken by helicopter to Crosshouse Hospital and, after recovering in a high dependency ward, was transferred to the psychiatric wing but noted only as being at risk of absconding, not taking her life.
A healthcare assistant told investigators: "If I'd known she was a suicide risk I'd never have taken my eyes off her."
Window restrictors had earlier been identified as a danger and all had been replaced apart from Ms Black's room, which is thought to have been occupied and overlooked by contractors.
She hanged herself from the fittings with her bootlaces on August 31, 2010 while staff sat outside in the corridor with only a partial view of the ward.
An assistant who "sensed something was wrong" ran into the room and took Ms Black's weight until she was freed, but she could not be revived.
Sheriff Murphy extended his sympathy to Ms Black's parents in court, telling them that despite the passage of four years it could not have been easy to hear how their daughter's death was avoidable.
He described the "systemic failure" and degree of foreseeability that reached up into management, adding: "I regard these failures as serious."
Outside court, Ms Black's parents Ian and Janette, formerly of Eaglesham, Renfrewshire, but now of Kent, paid tribute to their daughter, a qualified Steiner schools teacher who taught yoga to children, worked in America and was "creative and full of energy".
Mr Black, 65, a former personnel director at Glasgow University, said: "As the hearing found, there was inadequate communication. Procedures were in place but not followed through.
"Nobody seemed to communicate to the healthcare assistants and I think there should have been closer observation from qualified staff."
Mrs Black, 68, a retired social services team leader with East Renfrewshire Council, said: "No amount of fine will bring our daughter back but the important thing is for lessons to be learned, and I'm not entirely confident that will happen.
"The risks were self-evident. If you helicopter a patient from Arran unconscious, having taken a massive overdose, to me and to the man in the street, that shouts 'risk.'"
A spokeswoman for NHS Ayrshire and Arran said: "We take seriously any failures in care and have made numerous changes to our processes. We have undertaken a significant training programme with our staff since this incident,a point noted by the sheriff in his judgement."