  We consider a class of $(N,M)$-elementary step functions on the $p$-adic
Vilenkin group. We prove that $(N,M)$-elementary step function generates a MRA
on $p$-adic Vilenkin group iff it is generated by a special $N$-valid rooted
tree on the set of vertices $\{0,1,\dots p-1\}$ with the vector $(0,...,0)\in
\mathbb Z^N$ as a root. Bibliography: 15 titles.
