  In this article we construct Weil representations of quasi-split unitary
groups $U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$ associated to quadratic
extensions of finite fields. We define these representations by using an
adequate presentation Bruhat like of those groups. More precisely, we define
Weil representations of $U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$ associating to
each generator a linear map of a suitable $\mathbb{C}$-vector space satisfying
the relations of the aforementioned presentation. In addition, we also address
the natural question on the compatibility of our representation of
$U(n,n)(\mathbb{F}_{q^2}/\mathbb{F}_q)$ with the classical one constructed by
G\'erardin.
