This article mainly focuses on presenting a new accurate technique (Fourier Transform Meth-od) for solving linear of mth order Difference Equations with constant coefficients. Also, a new lower triangular matrix was introduced to overcome problems related to finding the Fourier Transform of polynomials by rewriting standard-based polynomials through the fallen power polynomial base. Besides, five examples have been presented to illustrate the validity and ac-curacy of this method. The results reveal that the Fourier transform method is very effective and attractive in solving the difference equations.