  The equivalence of tripartite pure states under local unitary transformations
is investigated. The nonlocal properties for a class of tripartite quantum
states in $\Cb^K \otimes \Cb^M \otimes \Cb^N$ composite systems are
investigated and a complete set of invariants under local unitary
transformations for these states is presented. It is shown that two of these
states are locally equivalent if and only if all these invariants have the same
values.
