The main problem in differentiator design is to combine differentiation exactness with robustness in respect to possible measurement errors and input noises. The proposed differentiator provides for proportionality of the maximal differentiation error to the square root of the maximal deviation of the measured input signal from the base signal. Such an order of the differentiation error is shown to be the best possible one when the only information known on the base signal is an upper bound for Lipschitz＇s constant of the derivative.