  We have previously developed the BRST quantization on the hypersurface
$V_{N-1}$ embedded in N dimensional Euclidean space $R_N$ in both Hamiltonian
and Lagrangian formulation. We generalize the formalism in the case of L
dimensional manifold $V_L$ embedded in $R_N$ with $1\leq L < N$. The result is
essentially the same as the previous one. We have also verified the results
obtained here using a simple example of particle motion on a torus knot.
