  Any bipartite entanglement witness $W$ can be written as
$W=c_{\sigma}I-\sigma$, where $\sigma$ is a quantum state, $I$ is the identity
matrix, and $c_{\sigma}$ is a non-negative number. We present a general method
to extend the given entanglement witness to multipartite cases via
purification, partial purification, and direct tensor of the quantum state
$\sigma$. Our methods extend $\sigma$ but leave the parameter $c_{\sigma}$
untouched. This is very valuable since the parameter is generally not easy to
compute.
