The Order was founded by Hugues de Payns, a French Knight, after the First Crusade of 1099 to protect pilgrims on the road to Jerusalem. Its headquarters was the captured Al-Aqsa mosque on the Temple Mount, which lent the Templars their name.
But when Jerusalem fell to Muslim rule in 1244, rumors surfaced that the knights were heretics who worshipped idols in a secret initiation ceremony.
In 1307, King Philip IV "the Fair" of France, in desperate need of funds, ordered the arrest and torture of all Templars. After confessing various sins their leader, Jacques de Molay, was burnt at the stake.
Pope Clement V then dissolved the order and issued arrest warrants for all remaining members. Ever since, the Templars have been thought of as heretics.
The new book is based on a scrap of parchment discovered in the Vatican's secret archives in 2001 by Professor Barbara Frale. The long-lost document is a record of the trial of the Templars before Pope Clement, and ends with a papal absolution from all heresies.
Professor Frale said: "I could not believe it when I found it. The paper was put in the wrong archive in the 17th century."
The document, known as the Chinon parchment, reveals that the Templars had an initiation ceremony which involved "spitting on the cross", "denying Jesus" and kissing the lower back, navel and mouth of the man proposing them.
The Templars explained to Pope Clement that the initiation mimicked the humiliation that knights could suffer if they fell into the hands of the Saracens, while the kissing ceremony was a sign of their total obedience.
The Pope concluded that the entrance ritual was not truly blasphemous, as alleged by King Philip when he had the knights arrested. However, he was forced to dissolve the Order to keep peace with France and prevent a schism in the church.
"This is proof that the Templars were not heretics," said Prof Frale. "The Pope was obliged to ask pardon from the knights.
"For 700 years we have believed that the Templars died as cursed men, and this absolves them."
As a teenager I was a member of the DeMolay.