| Let $G$ be the finite cyclic group $Z_{2}$ and $V$ be a vector space of dimension $2n$ with basis $x_{1},\ldots,x_{n},y_{1},\ldots,y_{n}$ over the field $F$ with characteristic 2. If $\sigma$ denotes a generator of $G$, we may assume that $\sigma(x_{i})=ay_{i}$, $\sigma(y_{i})=a^{-1}x_{i}$, where $a\in F^{*}$. In this paper, we describe the explicit generator of the ring of modular vector invariants of $F[V]^{G}$. We prove that $$F[V]^{G}=F[l_{i}=x_{i} ay_{i}, q_{i}=x_{i}y_{i},1\leq i\leq n,M_{I}=X_{I} a^{|I|}Y_{I}],$$ where $I\subseteq A_{n}=\{1,2,\ldots,n\}$, $2\leq |I|\leq n$. |
