  In this paper we construct vector bundles associated to monads on
$X=\mathbb{P}^n\times\mathbb{P}^n\times\mathbb{P}^m\times\mathbb{P}^m$. We
first establish the existence of such monads on $X$. Once the monads exist, the
next natural question is whether the cohomology vector bundle associated to
these monads are simple or not. We study these vector bundles associated to
monads and prove their stability and simplicity.
