The equation proposed by Augis and Bennett for determining the kinetic exponent of the Johnson-Mehl-Avrami UMA) model is thoroughly analyzed; a new expression, calculated accurately with no assumptions introduced, is proposed. This new method of calculation has been extended to the different kinetic models more commonly used in the literature for describing solid-state reactions. However, determining the JMA exponent from the Augis and Bennett method can lead to an incorrect interpretation of the reaction mechanism unless an additional, independent test is used. A testing method for verifying the applicability of the Augis and Bennett method is proposed. The kinetic analysis of the crystallization of Ge0.3Sb1.4S2.7 has been used for checking this method.