本文指出：如果有两个*运算使得同一个实Banach代数均成为实C*-代数，则这两个*运算必然是相同的，即实C*-代数中*运算是唯一的．

In this paper, we point out that the two * operations must be same if there are two * operations which make the same one real Banach algebra be a real C*-algebra at the same time. i.e. the * operation in a real C*-algebra is uniquely determined.