Lifting scheme is not only a fast algorithm of existing wavelet transforms

but also a tool to produce new wavelet transforms. Multiwavelets are a new kind of wavelets and have found many new applications to signal processing. In this paper we present a framework of lifting scheme for multiwavelet transforms

in which the existing lifting schemes designed originally for wavelet (not multiwavelet) transforms can be used as building blocks. Thus we needn't concern about the internal structures and parameters of these building blocks. What we need to do is to choose different wavelets for different applications and then make use of the lifting schemes for these wavelets to build a new lifting scheme. This new lifting scheme is equivalent to a multiwavelet transform. We build such a lifting scheme by using the lifting schemes for D9/7 biorthogonal wavelet transform and then apply this new lifting scheme to image coding. We have achieved better results than that obtained by the commonly-used GHM multiwavelet image coding.