Detectives investigating the murder of Siobhán Kearney in south Dublin on Tuesday believe her killer strangled her and then arranged the scene to make it appear she had taken her own life.
Gardaí believe Ms Kearney, a 38-year-old married woman with one child, was strangled with the flex of a vacuum cleaner in the bedroom of her home in the Knocknashee estate in Goatstown.
She had lived in Dublin for periods of the year with her husband, Brian, and three-year-old son Dan.
The couple owned a hotel in Majorca and spent most of their time there.
A man was arrested on Thursday morning in connection with the murder. He was detained under Section 4 of the Criminal Justice Act at Dundrum Garda station. He was released on Thursday night, and a file is being prepared for the Director of Public Prosecutions.
Gardaí initially believed Ms Kearney may have taken her own life.
However, a postmortem examination found that she had been strangled.
Detectives investigating the murder believe her killer was known to her.
A caller to the house on Tuesday morning alerted gardaí, who arrived on the scene and discovered the woman's body.
Ms Kearney and her husband owned an upmarket hotel in the remote Sóller region of Majorca.They bought it in late 2002 and opened it in early 2003.
Ms Kearney had trained as a chef in the Shelbourne Hotel, Dublin, and set up her own catering business in Dublin in the early 1990s.
Last March she was one of a number of Irish people featured in The Irish Times Saturday magazine, in which Irish people wrote about relocating abroad.
"I suppose it's difficult to detach ourselves from the business," she said. "We don't have a normal home life because we've got guests staying with us all the time, but that's the nature of the hospitality business.
"We're on call 24 hours a day. But the summers are fantastic - breakfast al fresco every day is hard to beat."
