  In this paper, we consider the geodesic flow on factors of the hyperbolic
plane. We prove that a periodic orbit including a 2-antiparallel encounter has
a partner orbit. We construct the partner orbit and give an estimate for the
action different between the orbit pair. Then we apply the result to reprove
the accuracy of Sieber/Richter's prediction in [Sieber and Richter, 2001].
