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Using string field theory, we argue that the tachyon potential on a D-brane in bosonic string theory in arbitrary background has a universal form, independent of the boundary conformal field theory describing the brane. This implies that if at an extremum of the tachyon potential the total energy of the brane vanishes in a particular background, then it vanishes in any other background. Similar result holds for the tachyon potential of the D-brane anti-D-brane system and the non-BPS D-brane of type II string theory.