This paper investigates multiwavelet image coding. Firstly
unlike many papers on multiwavelets
we describe multiwavelets from the viewpoint of Mallat's frame of multiresolution analysis and deduce a fast algorithm of multiwavelet transform. Secondly
combining two preprocessing methods of multiwavelet transform of images commonly used in many papers
we propose a new preprocessing method. Lastly
we reveal the dependence between different components of a vector-subimage emerged after multiwavelet transforming an image and perform image coding based on this dependence. The theoretical analysis and experimental results presented in this paper show that multiwavelet image coding is a promising way to compress an image.