Physics suggests equal amounts of matter and antimatter should have been made in the Big Bang.
In 2010, researchers at the Tevatron accelerator claimed preliminary results showing a small excess of matter over antimatter as particles decayed.
The team has submitted a paper showing those results are on a firmer footing.
Each of the fundamental particles known has an antimatter cousin, with identical properties but opposite electric charge.
When a particle encounters its antiparticle, they "annihilate" each other, disappearing in a high-energy flash of light.
The question remains: why did this not occur in the early Universe with the equal amounts of matter and antimatter, resulting in a Universe devoid of both?
The Tevatron results come from a shower of particles produced at the facility when smashing protons into their antimatter counterparts, antiprotons.
The proton-antiproton collisions in turn create a number of different particles, and the team operating the Tevatron's DZero detector first noticed a discrepancy in the decay of particles called B mesons.
These decayed into pairs of particles called muons alongside pairs of their antimatter versions, antimuons. But, as the team reported in May 2010 in a paper published in Physical Review Letters, there was a notable 1% excess of the matter particles.
However, unpicking important events in the soup of interactions created in particle physics experiments meant that those measurements were associated with a level of uncertainty - reflecting the probability that the effect they see is a random statistical occurrence, rather than new physics.
The researchers now have 50% more data to work with, and have tried to establish that their earlier result in fact came from the particle decays that they first proposed.
As they reported this Thursday, they have now reduced the uncertainty in their experiment to a level of "3.9 sigma", or 3.9 standard deviations - equivalent to a 0.005% probability that the effect is a fluke.
But particle physics has a strict definition for what may be called a discovery - the "five sigma" level of certainty, or about a 0.00003% chance that the effect is not real - which the team must show before they can claim to have solved the long-standing matter/antimatter mystery.

Police found the injured 18-year-old after they were called to Hertford Road, Enfield, on Saturday at 22:30 BST over reports of a fight.
He was taken to hospital but was pronounced dead an hour later. Two others also suffered stab wounds.
In a separate incident, a man was shot and stabbed to death in broad daylight near Bow Road Tube station.
The victim, 41, was killed in Eagling Close on Saturday afternoon in what police described as a "violent murder".
Two men have been arrested and are in custody at east London police stations.
The two teenagers who were stabbed in Enfield were found in Palmers Lane.
The 17 and 19-year-olds were taken to hospital but their injuries are not being treated as life-threatening.
Scotland Yard said no arrests have been made and have appealed for witnesses.
In another incident earlier, a man was taken to hospital in a life-threatening condition after being stabbed in the head and neck in Enfield.
Police said they believe the victim, who is thought to be aged in his 30s, was attacked following an "altercation" with a group of men in Exeter Road.
No arrests have been made.
US particle physicists are inching closer to determining why the Universe exists in its current form, made overwhelmingly of matter.
[NEXT_CONCEPT]
A man has been stabbed to death and two others injured during a large brawl in north London.