  We have proposed a method to calculate the relative magnetic helicity in a
finite volume as given the magnetic field in the former paper (Yang et al. {\it
Solar Physics}, {\bf 283}, 369, 2013). This method requires that the magnetic
flux to be balanced on all the side boundaries of the considered volume. In
this paper, we propose a scheme to obtain the vector potentials at the
boundaries to remove the above restriction. We also used a theoretical model
(Low and Lou, {\it Astrophys. J.} {\bf 352}, 343, 1990) to test our scheme.
