  Based on the orthogonal Labastida-Mari{\~n}o-Ooguri-Vafa conjecture made by
L. Chen & Q. Chen [5], we derive an infinite product formula for Chern-Simons
partition functions, which generalizes the Liu-Peng's [19] recent results to
the orthogonal case. Symmetry property of this new infinite product structure
is also discussed.
