In the present work, through the path integral of Gaussian type correlation function, a new formalism based on Fermi-Golden Rule for calculating the rate constant of nonradiative decay process with Duschinsky rotation effect in polyatomic molecules is developed. The advantage of the present path-integral formalism is promoting-mode free. In order to get the rate constant, a "transition rate matrix" needs to be calculated. The rate constant calculated previously is only an approximation of diagonal elements of our "transition rate matrix " . The total rate should be the summation over all the matrix elements.
