For functionsf which have an absolute continuous (n−1)th derivative on the interval [0, 1], it is proved that, in the case ofn>4, the inequality ‖‖f(n−2)‖‖∞⩽4n−2(n−1)!‖f‖∞+‖‖f(n)‖‖∞/2 holds with the exact constant 4 n−2(n−1)!.