A fast a1gorithm for computing N×M 2D-DCT(Ⅱ) is deve1oped. The amount of the real operations are:M_u=1/2NMlog₂N+1/4MNlog₂M,A_d=3/2NMlog₂NM-3MN-1/2M²+M+N,where N=2^t,M=2^r.When N=M,the result is the same as in [5],which is the best result at present. But the algorithm in [5] has instability leading to large errors easily.This limitation has been overcome in the paper. We also derive some algorithms about 2D-DCT,2D-DST,2D-DCST. A fast algorithm about 2D-DFT is developed in particular,the amount of the operations in paper is similar to that in [1] with FPT to calculate 2D-DFT.