  The effects of Umklapp scattering on the zero-temperature conductance in
one-dimensional quantum wires are reexamined by taking into account both the
screening of external potential and the non-uniform chemical potential shift
due to electron-electron interaction. It is shown that in the case away from
half-filling the conductance is given by the universal value, $2e^2/h$, even in
the presence of Umklapp scattering, owing to these renormalization effects of
external potential. The conclusion is in accordance with the recent claim
obtained for the system with non-interacting leads being attached to a quantum
wire.
