A baby born at Cavan General Hospital yesterday has died.
The HSE is to launch an investigation after they confirmed the baby's death.
The HSE said in a statement: "As is normal practice a full review of the circumstances surrounding the death will be carried out.
"The hospital will give the family every assistance and support required."
It brings to three the number of infant deaths linked to the hospital in the past 18 months. In November 2012, a child was born at Cavan General Hospital and transferred to a Neonatal Unit in the Rotunda Hospital in Dublin where he later died.
A separate investigation is already underway following the death of a newborn baby at the hospital on April 26 in a "clinical incident".
In a statement a HSE spokeswoman said: "Cavan and Monaghan Hospital management would like to offer its deepest sympathy to the family on their tragic loss and hope they will be given the privacy that they need to deal with their grief. The hospital will give the family every assistance and support required.
The family of the baby have asked that the media to respect their privacy to "allow them mourn their loss without further media attention", according to the spokeswoman.
Asked to comment on concerns that this latest infant death raise for the safety and level of care at the hospital the HSE spokeswoman declined to comment further.