  In their unpublished work, Jockusch and Propp showed that a 2-enumeration of
antisymmetric monotone triangles is given by a simple product formula. On the
other hand, the author proved that the same formula counts the domino tilings
of the quartered Aztec rectangle. In this paper, we explain this phenomenon
directly by building a correspondence between the antisymmetric monotone
triangles and domino tilings of the quartered Aztec rectangle.
