  A coordinate-choice independent expression does not depend how the magnetic
surface is parametrized by (\theta,\zeta). Flux-force relation in neoclassical
toroidal viscosity(NTV) theory has been generalized in a coordinate-choice
independent way. The expression for the surface averaged drift orbit flux in
1/\nu regime is derived without the requirement of straight field line
coordinates. The resulted formula is insensitive to how the magnetic surface is
parametrized and broadens the cases where flux-force relation can be applied.
Construction of straight field line coordinates is avoided when the formula is
used for numerical computation.
