A new DFT fast algorithm of the multidimension signal is presented in this paper.Because it transfrom multidimension signal DFT into many groups of one dimension odd frequency DFT

the number of the total operation depends mainly on one dimension odd frequency FFT algorithm.It has better regularity structure and can operate in-place.Under two dimension

compared with polynomial transform

both is the same when data are real;the new algorithm is somewhat better than Reference[6] in number of add operation when data are complex. The number of the total operation of 3-D and 4-D is also given.