The concept of 2D matrix is extended to 4D matrix using multi dimensional matrix theory. 4D n^th order Walsh orthogonal transform is formed and is applied on image along with cosine transform. The model of 4-D n^th order matrix can process 4-D data in a unified mathematical model. It has high efficiency of classical matrix transform in the aspect of removing redundancy of color space. So this transform found effective than jpeg standards in color image coding there by compression.

Keywords:Multidimensional matrix, 4D n^th order Walsh transform, orthogonal matrix, coding of coefficients, compression.