The total photodetachment cross section of a linear triatomic negative ion using plane polarized laser light parallel to the axis of the molecular ion is derived. The cross section shows strong oscillations in contrast to the recently reported case, where the laser polarization was perpendicular to the axis of the triatomic molecular ion (Appl. Phys. Lett. 94, 041125, 2009). Closed orbit theory is used to explain these oscillations and the results are compared with a diatomic molecule.