  In this paper we propose a symmetric q-deformed Tamm-Dancoff (S-TD)
oscillator algebra and study its representation, coordinate realization, and
main properties. In particular, the non-Fibonacci (more exactly,
quasi-Fibonacci) nature of S-TD oscillator is established, the possibility of
relating it to certain p,q-deformed oscillator family shown, the occurrence of
the pairwise accidental degeneracy proven. We also find the coherent state for
the S-TD oscillator and show that it satisfies completeness relation. Main
advantage of the S-TD model over usual Tamm-Dancoff oscillator is that due to
(q<-->q^{-1})- symmetry it admits not only real, but also complex (phase-like)
values of the deformation parameter q.
