  In this Letter we suggest a method of convex rigid frames in the studies of
the multipartite quNit pure-states. We illustrate what are the convex rigid
frames and what is the method of convex rigid frames. As the applications we
use this method to solve some basic problems and give some new results (three
theorems): The problem of the partial separability of the multipartite quNit
pure-states and its geometric explanation; The problem of the classification of
the multipartite quNit pure-states, and give a perfect explanation of the local
unitary transformations; Thirdly, we discuss the invariants of classes and give
a possible physical explanation.
