Known as ABBA, the system is designed to prevent the team that goes second from being put at the psychological disadvantage of always having to play catch-up.
Currently penalty shootouts see team A and team B take five penalties each in an alternating pattern with sudden death used after that if the scores are level.
Football's rule making body IFAB, which approved trials of the new system in March, says research proves the team taking the first penalty have a 60 percent chance of winning, giving them an unfair advantage.
Instead, IFAB want to try a new sequence that replicates the switch of serve between tennis players in a tie break.
It involves team A taking the first penalty, team B the second and third, team A the fourth and fifth and so on until each team had taken five. The sequence would continue if the shootout then goes to sudden death.
"The hypothesis is that the player taking the second kick in the pair is under greater mental pressure," said UEFA.
"If the opposition's first penalty in the pair has been successful, a miss by the second penalty-taker in the pair could mean the immediate loss of a match for his team, especially from the fourth pair of penalties onwards." UEFA said.
UEFA said the system was also being tried at the women's European under-17 championship, which began in the Czech Republic on Tuesday.
As with the existing system, the referee will toss a coin to decide at which end of the pitch the shootout takes place.
The referee will then toss the coin for a second time and winners can decide whether to take the first or second kick.
(Writing by Brian Homewood, editing by Larry King)
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