A new modulated hopping Discrete Fourier Transform (mHDFT) algorithm which is characterized by its merits of high accuracy and constant stability is presented. The proposed algorithm, which is based on the circular frequency shift property of DFT, directly moves the k-th DFT bin to the position of k = 0, and computes the DFT by incorporating the successive DFT outputs with arbitrary time hop L. Compared to previous works, since the pole of mHDFT precisely settles on the unit circle in the Z-plane, the accumulated errors and potential instabilities, which are caused by the quantization of the twiddle factor, are always eliminated without increasing much computational effort. The numerical simulation results verify the effectiveness and superiority of the proposed algorithm.