The Boeing 747s were 30 miles north of Glasgow and converging on each other side-by-side for 10 miles. An air traffic controller ordered the plane on the left to make a left turn and the one on the right to turn right. But they did the opposite - bringing the two aircraft closer.
A crash, on June 23 this year, was only averted when the pilots saw the others' planes and took action.
A report by the UK Air-prox Board, which examines near misses said the board was surprised all four pilots had "misheard or misinterpreted the avoiding action".