  In this paper we quantize the free-particle on a D-dimensional sphere in an
unambiguous way by converting the second-class constraint using St\"uckelberg
field shiftting formalism. Further, we argument that this formalism is
equivalent to the BFFT constraint conversion method and show that the energy
spectrum is identical to the pure Laplace-Beltrami operator without additional
terms arising from the curvature of the sphere. We work out the gauge symmetry
generators with results consistent with those obtained through the nonlinear
implementation of the gauge symmetry
