  Let {\phi} be an arbitrary generalized Gaussian (squeezed coherent state),
{\Lambda}_{{\alpha}{\beta}}=({\alpha}_1 Z \times\cdot\cdot\cdot\times
\alpha_{n}\mathbb{Z)\times}(\beta_{1}\mathbb{Z}\times\cdot\cdot\cdot
\times\beta_{n}\mathbb{Z)}$ a rectangular lattice. We show that there exists a
positive definite symplectic matrix M (depending on {\phi}) such that the
multivariate Weyl--Heisenberg system G({\phi},M{\Lambda}_{{\alpha}{\beta}}) is
a frame. In a forthcoming Note we will prove a converse to this result.
