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.