Its "tails" at the back are black and are said to mourn the killing of Michael Collins, who was in an Armoured Car Corps Rolls-Royce when he was mortally wounded.
The distinctive Glengarry cap has been issued to Cavalry Corps members since it was formed in 1934.
Some military observers claim the black tails are to mourn the killing of General Collins.
However, a Defence Forces spokesman said the tails are not believed to have any particular significance.
The Glengarry was adopted for troopers getting in and out of armoured cars.
Lt Gen McCann is the first Cavalry Corps officer to be appointed to the Defence Forces' top job in 50 years.
The last Cavalry Corps officer to occupy the position was General Sean Collins-Powell.
The Glengarry differs from its Scottish counterpart by being more of a caubeen with tails, experts say.
COMBAT Lt Gen McCann wore the beret along with his issue DPM camouflage combat uniform during a visit to troops in Cathal Brugha Barracks, Rathmines.
McCann (59) is a former Director of Cavalry. Cathal Brugha Barracks is home to two cavalry outfits, including 2nd Cavalry Squadron, which provides the Presidential Escort of Honour.
The Reserve's 62nd Cavalry Squadron is also based in Rathmines.
He accompanied Defence Minister Tony Killeen on a visit to the barracks where the minister inspected a guard of honour.
Lt Gen McCann (59) has been Deputy Chief of Staff, Operations, since 2009.
He has served in Lebanon, the Iraq Kuwait observer mission and the EU Monitoring Mission in Sarajevo in 2000.
In 2003, he was appointed Chief Operations Officer with UNTSO, the UN Truce Supervisory Organisation.
Lt Gen McCann lives in Newbridge, Co Kildare, and is married to Frances. They have two sons, one of whom is currently serving in the Defence Forces.
He served as personal assistant to one of the army's most progressive chiefs, Lt Gen Gerry McMahon.