The role of serial correlations in time series analysis is well known. Considerable attention has been given to the derivation of their sampling properties when the sample size is both small and large. In all these discussions it has been tacitly assumed that these correlations are bounded between -1 and 1. At least, no literature exists which considers it otherwise. Whereas it is true that the serial correlations are bounded it is not true that the bounds are -1 and 1. In fact, in small samples these bounds may very well be lower than -1 and higher than 1. To the best of the author's knowledge, this fact has not been mentioned anywhere. The purpose of this note is to discuss this particular aspect.