The modified discrete cosine transform (MDCT) and modified discrete sine transform (MDST) are employed in subband/transform coding schemes as the analysis/synthesis filter banks based on time domain aliasing cancellation. Princen, Bradley, and Johnson defined two types of MDCT, specifically, for an evenly stacked and an oddly stacked analysis/synthesis system. A new unified fast algorithm for the forward and inverse MDCT/MDST computation in the evenly stacked system is proposed. It is based on the DCT of type II (DCT-II) and the DST of type IV (DST-IV), and uses real arithmetic only. The corresponding generalized signal flow graph is regular and structurally simple and enables one to compute alternate MDCT/MDST and their inverses in general for any N divisible by 4 (N being the length of a data sequence).