  We demonstrate the existence of a set of novel off-shell nilpotent and
absolutely anticommuting continuous symmetry transformations, within the
framework of the Becchi-Rouet-Stora-Tyutin (BRST) formalism, which are over and
above the usual off-shell nilpotent and absolutely anticommuting (anti-)BRST
symmetry transformations that are respected by the first-order Lagrangian for
the Friedberg-Lee-Pang-Ren (FLPR) model that describes the motion of a
non-relativistic particle of unit mass moving under the influence of a general
rotationally invariant spatial two-dimensional potential. We christen these
novel set of fermionic symmetry transformations as the (anti-)co-BRST symmetry
transformations because the gauge-fixing term remains invariant under them. We
derive the conserved and off-shell nilpotent (anti-)BRST and (anti-)co-BRST
charges and comment on the physicality criteria w.r.t. them where we establish
the presence of the operator forms of the first-class constraints (of the
original classical gauge theory) at the quantum level.
