This paper follows the format of our tutorial on multivariate wavelet decomposition, . We demonstrate here that the methods employed by Jia and Micchelli  can be extended to subspaces of L
) generated by a finite number of compactly supported functions. Specifically, we let Φ: ℝs
→ ℂN be a vector of N functions Φ = (φ1,…,φN
). AS in our previous article in these proceedings we will be ... [Show full abstract] concerned with wavelet decomposition in L
2(ℝs) built upon Φ and the basic operations of shift and scale. All the results in  pertain to the case N = 1. We now proceed to extend them to general N.