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It is well known that the x-condition number of a linear operator is a measure of ill condition with respect to its generalized inverses and a relative error bound with respect to the generalized inverses of operator T with a small perturbation operator E, namely,\|(T+E)^+-T^+\|\|T^+\|≤ x(T)\|E\|\|T\| 1-x(T)\|E\|\|T\| , where xT=\|T\|\|T^+\|. The problem is whether there exists a positive number μ(T) independent of E but dependent on T such that the above relative error bound holds and μ(T)＜x(T). In this paper, an answer is given to this problem. , number=4, journal=Journal of Computational Mathematics, year=2021, month=July, pages=316–324