  We study entanglement witness and present a construction of entanglement
witnesses in terms of the mutually unbiased measurements (MUMs). These
witnesses include the entanglement witnesses constructed from mutually unbiased
bases (MUBs) as a special case. Comparing with the dimension dependence of
MUBs, the witnesses can be always constructed from a complete set of $d+1$ MUMs
for any dimension $d$. We show that our witness can detect entanglement better
than previous separability criterion given also by MUMs. And the approach can
be experimentally implemented.
