New figures show that 9,727 people left emergency departments without completing their treatment in May.
That's 7.7 per cent of all presentations at EDs.
There's a big variation across the country - the highest was nearly 18 per cent in Tallaght University Hospital in Dublin.
Naas General Hospital in Co Kildare and St James's Hospital in Dublin both had over 12 per cent.
But eight hospitals had rates of less than 5 per cent.
Sinn Féin's health spokesman, David Cullinane, says the problem is partly down to overcrowding:
"There's a clear correlation between the hospitals that have the highest wait times and the hospitals that have the highest number of patients who left without getting treatment or without being seen".
The HSE says Emergency Departments are for people with serious injuries or illnesses, but many others go there when they do not need to.
It says patients are treated by priority and, because of that, some patients with less serious needs may choose to get healthcare elsewhere.
