  We show that the integrability of the $SO(N)/SO(N-1)$ Principal Chiral Model
(PCM) originates from the Pohlmeyer reduction of the $O(N)$ Non Linear Sigma
Model (NLSM). In particular, we show that the Lax pair of the PCM is related
upon redefinitions and identification of parameters to the zero curvature
condition, which is a consequence of the flatness of the enhanced space used in
the Pohlmeyer reduction. This identification provides the solution of the
auxiliary system that corresponds to an arbitrary NLSM/PCM solution.
