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Rare-earth tritellurides, RTe₃, studied for long time a canonical charge density wave (CDW), while their square-net nature was suggested to host unique quantum geometry. This has led to the recent discovery by our group of the Axial Higgs mode in LaTe₃ and GdTe₃, suggesting the CDW is unconventional. Here we explore ErTe₃, which shows the orthogonal bidirectional CDW, using Raman scattering. Surprisingly, we find the amplitude mode corresponding to primary and secondary CDW has different underlying symmetry of the order parameter strongly suggesting that the onset secondary CDW is not just the 90 degree rotated analogue of the primary CDW order. Furthermore, the circular polarized Raman study shows the appearance of the secondary CDW mode only in the crossed circular polarization configuration confirms that it has angular momentum. Our results shed light on the unconventional nature of the CDW in ErTe₃ and highlight the rich physics associated with these square-net quantum materials.