  We introduce a sufficient and necessary condition for the separability of a
specific class of $N$ $d$-dimensional system (qudits) states, namely special
generalized Werner state (SGWS): $W^{[d^N]}(v)=(1-v)\frac{I^{(N)}}{d^N}+v|\psi
_d^N><\psi_d^N|$, where $ |\psi_d^N>=\sum_{i=0}^{d-1}\alpha_i|i... i>$ is an
entangled pure state of $N$ qudits system and $\alpha_i$ satisfys two
restrictions: (i) $\sum_{i=0}^{d-1}\alpha_i\alpha_i^*=1$; (ii) Matrix
$\frac{1}{d}(I^{(1)}+\mathcal{T}\sum_{i\neq j}\alpha_i|i>< j|\alpha_j^*)$,
where $\mathcal{T}=\texttt{Min}_{i\neq j}\{1/|\alpha_i\alpha_j|\}$, is a
density matrix. Our condition gives quite a simple and efficiently computable
way to judge whether a given SGWS is separable or not and previously known
separable conditions are shown to be special cases of our approach.
