The charge balance function is studied in Au + Au collisions at √sNN = 200 GeV using the STAR detector at the Relativistic Heavy-Ion Collider. Within the acceptance of the STAR TPC, it is found that the balance function is independent of the position of pseudorapidity windows with equal-size. It is also demonstrated for the first time at RHIC that the balance function divided by a scaling factor related to pseudorapidity is independent of the width and position of the pseudorapidity window. Moreover, Such a scaled balance function is further f...