Anti-poverty campaign group, Turn2Us, said parents being unable to register their newborns during the pandemic is likely the main cause across the UK.
HM Revenue and Customs data shows families were receiving the benefit for 1,135 children less than one year old in Falkirk as of August last year.
This was 9% fewer than at the same point in 2019, and a bigger drop than the 3% seen the year before.
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Across the UK, the number of child benefit claims for infants fell by 9% to 513,445, which was the biggest decrease of all children up to 19.
Overall, the number of children for whom benefits were being received across the UK fell by just 1% between both 2018 and 2019, and 2019 and 2020.
In Falkirk, the figure fell from 28,265 to 27,725 between August 2019 and last year – a drop of 2%.