Local Gardai believe the grandmother was fatally attacked in her home near Killarney some time between last Friday and this Monday.
The man in his 50s who was arrested in connection with this killing has been released without charge pending further investigation.
He was arrested on Tuesday evening, shortly after the investigation into Miriam Burns’ death was declared a murder inquiry.
Gardai are understood to have searched an area around an old holy well near Killarney in connection with the investigation.
Ms. Burns, who was 75, has been remembered as a ‘smiling’ and ‘stylish’ lady who often cycled to and from her engagements around the town.
She’s described as a 'devoted' family woman in her death notice, who is ‘devastatingly missed’.
The grandmother will be laid to rest at St Mary’s Cathedral on Sunday afternoon at 2.15pm.