Symmetry analysis which is associated with Sophus Lie is one of the approaches of solution of an evolution partial differential equation. This paper extends the generator for the n-th prolongation of the generator of an n-th–order ordinary differential equation to a general formula for the n-th prolongation of a generator, , with k-independent and p-dependent variables of an n-th-order partial differential equation. With this formula, the cumbersomeness in the initial extraction of determining equations from the process of obtaining a solution is reduced.