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We have proposed a method to calculate the relative magnetic helicity in afinite volume as given the magnetic field in the former paper (Yang et al. {\itSolar Physics}, {\bf 283}, 369, 2013). This method requires that the magneticflux to be balanced on all the side boundaries of the considered volume. Inthis paper, we propose a scheme to obtain the vector potentials at theboundaries 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.

Method of Relative Magnetic Helicity Computation II: Boundary Conditions for the Vector Potentials