In 2000-2001, Arsenal and Chelsea had the same UEFA coefficient and then are tied. UEFA ranking is (1, 4, 2, 2) for 2000-2001, what means that Manchester United is the first, Liverpool is the last, and the two intermediate positions are for Arsenal and Chelsea in an unknown order.
In 2009-2010, Liverpool and Arsenal have also the same UEFA coefficient, the ranking is (1, 2, 2, 4).