New figures from the Central Statistics Office show that manufacturing production rose by 0.4% in January from December.
But on an annual basis, production fell by 1.4% in January compared to the same month the previous year.
The CSO said that the modern sector - which is made up of high-technology and chemical sectors - rose by 1.6% on a monthly basis in January. But production in the sector was down 5.3% in the year with the expiry of certain patents a factor in the fall.
Production in the traditional sector increased by 3%. The traditional sector is more important for the domestic economy and accounts for two thirds of industrial sector jobs.
January saw the fourth consecutive increase, while production on an annual basis jumped 7.8% in the year in January.
Merrion economist Alan McQuaid said that the improvement in the UK economy and a recovery in sterling were key factors for the yearly increase in the traditional sector.
Meanwhile, the seasonally adjusted volume of industrial production for the three months from November to January was 0.2% higher than in the preceding quarter.
"We still firmly believe that when the world economy regains momentum, Ireland is better placed than most to take advantage of that. As regards 2014, we are optimistic that all things being equal, manufacturing output will post a modest single digit increase on 2013," the economist added.