A new graphical tool for checking normality of independently and identically distributed observations based on the third derivative T-3 of the logarithm of the empirical moment-generating function is proposed. A significant departure of this function from the horizontal zero line is indicative of non-normality. Behaviour in the neighbourhood of 0 indicates the type of departure from the normal distribution. Examples show that the T-3-method, when used in conjunction with the classical probability plot, can provide valuable insight into the data and be a powerful graphical tool.