  Let $P$ be a closed convex cone in $\mathbb{R}^{n}$. Assume that $P$ is
spanning i.e. $P-P=\mathbb{R}^{n}$ and pointed i.e. $P \cap -P=\{0\}$. Let
$\alpha:=\{\alpha_{x}:x \in P\}$ be a $\sigma$-weakly continuous family of
unital normal endomorphisms on $B(H)$. Denote the "product system" associated
to $\alpha$ by $\mathcal{E}_{\alpha}$. We show that $\mathcal{E}_{\alpha}$ is a
concrete product system and $\alpha$, up to cocycle conjugacy, can be recovered
completely from $\mathcal{E}_{\alpha}$
