  We derive necessary and sufficient conditions for the LU-equivalence of two
general (pure or mixed) $n$-qubit states as well as we determine the local
unitary operators connecting them. Almost all relevant information is contained
in the $1$-qubit reduced matrices of the multiqubit states under investigation
Our technique relies on identifying {\it ab initio} all local symmetries and
the corresponding local cyclic unitary operators. To derive the above
conditions we use the reference forms of the multiqubit states whose definition
requires the diagonalization of the 1-qubit reduced matrices. Based on those
conditions we propose a straightforward protocol to decide wether or not two
$n$-qubit states are LU-equivalent.
