  We revisit the genuine multipartite entanglement by a simplified method,
which only involves the Schmidt decomposition and local unitary transformation.
We construct a local unitary equivalent class of the tri-qubit quantum state,
then use the trace norm of the whole correlation tensor as a measurement to
detect genuine multipartite entanglement. By detailed examples, we show our
result can detect more genuinely entangled states. Furthermore, we generalize
the genuine multipartite entanglement criterion to tripartite
higher-dimensional systems.
