The mechanism of headache is not fully understood
Since 1913, when a scientist noticed that migraine was common in patients with high blood pressure, there has been a belief that an aching head could mean pressure was high.
However, in the latest study, scientists measured the blood pressure of well over 20,000 adults not prone to headache - and questioned them again more than a decade later.
As many as 28% of the volunteers confessed to suffering repeated headaches - one in four of these sufferers could be said to be having migraines.
However, the researchers found that those with higher than average blood pressures actually had a 30% lower chance of suffering headaches.
Reverse effect
The higher the blood pressure, the lower the chance of headache.
The researchers, from the Norwegian University of Science and Technology in Trondheim, wrote that it was possible, though unlikely, that headaches might be less common in those with high blood pressure because these people tended to go to the doctor more often and were therefore better looked after.
However, even excluding known high blood pressure patients, seemed to make no difference to the results.
However, they said it was more likely another phenomenon was at work.
They suggested that the blood pressure itself might be having the same effect as painkillers.
The system - called the baroreflex system - whose job it is to regulate arterial blood pressure within a narrow range, may, say the researchers, have an effect on the way the brain stem or spinal cord feels pain.
The study was published in the Journal of Neurology, Neurosurgery and Psychiatry.