Rumours of an alleged affair between two members of the Red Arrows were investigated by RAF bosses, a source has said.
Flight Lieutenant Kirsty Stewart, the first woman pilot in the aerobatic display team, and then- Squadron Leader Ben Murphy were interviewed to see if any rules had been broken when claims of a relationship between them emerged.
A source for the RAF said no action was taken following the 2011 inquiry.
"The two individuals were interviewed by their command chain and asked whether they were having an affair," he said.
"At that point, and the interviews given, it led to there being no action taken."
Asked if the RAF had a view on a report by The Sun newspaper that Flt Lt Stewart and Sqn Ldr Murphy were now engaged to be married, he said that the RAF does not discuss personal matters about any personnel.
He added: "They've all got their personal life and they're entitled to it."
Both fliers have now left the elite Red Arrows team.
Iraq veteran Flt Lt Stewart, 36, joined the display team for the 2010 season, having seen off competition from up to 40 other pilots.
She is now a Squadron Leader, having moved to a ground-based role following the tragic deaths of her Red Arrows team-mates Flight Lieutenant Jon Egging in August 2011 and Flight Lieutenant Sean Cunningham just three months later.
Mr Murphy, 38, who served in Iraq and Afghanistan, completed his term as team leader in 2011 and is now working for defence firm Lockheed Martin.