Breastfed babies are smarter because their mothers are clever in the first place, not because of any advantage of breastfeeding itself
Researchers found breastfeeding mothers tended to be more intelligent, more highly educated, and likely to provide a more stimulating home environment.
However, they stressed that there were still many advantages to breastfeeding.
The British Medical Journal study was carried out by the Medical Research Council and University of Edinburgh.
Lead researcher Geoff Der said: "This question has been debated ever since a link between the two [high IQ and breastfeeding] was first discovered in 1929.
"Breastfed children do tend to score higher on intelligence tests, but they also tend to come from more advantaged backgrounds."
The researchers analysed data from more than 5,000 children and 3,000 mothers in the US.
They found that mothers who breastfed tended to be more intelligent, and when this fact was taken into account, most of the relationship between breastfeeding and the child's intelligence disappeared.
The rest was accounted for by other aspects of the family background.
The researchers also looked at families where one child was breastfed and another was not.
This confirmed the earlier results - the breastfed child was no more intelligent than his or her sibling.
Putting the results together with other studies that measured the mother's IQ confirmed this pattern.
Mr Der said: "This research shows that intelligence is determined by factors other than breastfeeding.
"But breastfeeding has many benefits for both mother and child. It's definitely the smart thing to do."
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