An estimated 17,000 people contracted human swine flu in the last week, a reduction of around 10,000 cases compared with the previous week's figures according to the HSE.
The number of new hospitalisations has also declined.
There are 182 patients in hospital with the virus, 20 in intensive care.
No further deaths have been reported in the Republic, according to the HSE.
In Northern Ireland, two more adults have died from the virus, both with underlying health conditions, bringing the number of deaths there to 13.
Meanwhile, here the Irish Medical Organisation said that GPs are making steady progress towards completing their direct involvement in providing the human swine flu vaccination to people in the at risk categories.
Dr Ronan Boland, chairman of the IMO GP committee, said that when at risk groups have been vaccinated, at the request of the HSE, GPs will be using any surplus vaccine to immunise practice staff and other patients to minimise wastage.
The IMO has also welcomed the HSE's decision to start inviting children from six months to under five years and people aged 65 years and over to be vaccinated at HSE clinics.
Meanwhile, the Health Service Executive expects to begin vaccinating school children against Influenza A (H1N1) in schools from next week.
The Department of Education has written to all schools in the country advising them of the procedure.
The HSE will establish clinics in some schools, with pupils from neighbouring schools being invited to attend for vaccination.
Other students will be asked to attend their local HSE vaccination clinics.
The HSE says it is currently identifying the schools in which to establish clinics and says it is likely these schools will be the main post primary.
It says practical arrangements will be worked out locally with the individual schools.
Today's letter to schools from the Department of Education says the HSE will be distributing a vaccination information pack to schools for distribution to parents via their children.
The HSE says it expects vaccination to be completed by early 2010.
An estimated 300,000 people in the at risk category have been vaccinated against human swine flu.
The HSE says it is investigating less than a handful of cases where patients have been charged for the human swine flu vaccination by a GP.
Dr Kevin Kelliher of the HSE said that the vaccine is free and there is no charge for it to be administered as GPs are being paid for this.
More information on swine flu
