  In this paper we show the existence of a closed, embedded
$\lambda$-hypersurfaces $\Sigma \subset \mathbb{R}^{2n}$. The hypersurface is
diffeomorhic to $\mathbb{S}^{n-1} \times \mathbb{S}^{n-1} \times \mathbb{S}^1$
and exhibits $SO(n) \times SO(n)$ symmetry. Our approach uses a "shooting
method" similar to the approach used by McGrath in constructing a generalized
self-shrinking torus solution to mean curvature flow. The result generalizes
the $\lambda$-torus found by Cheng and Wei.
