This paper presents a new multi-dimensional Discrete Cosine Transform (DCT)?based coding to improve video coding efficiency. The technique proposes an application of additional DCT to the conventional twodimensional DCT coefficients after arranging multiple blocks of DCT coefficients of the same frequencies. Simulation results show that the proposed scheme improves PSNR by more than 2.6dB compared to 2-D, 4x4 transform used in the H.264 for similar bit rates. The proposed multidimensional DCT can easily be combined with existing coding techniques such as H.264 to achieve higher compression of video data.