  In this paper we establish the existence of monads on special Cartesian
products of projective spaces. Special in the sense that we mimick monads on
instanton bundles. We construct monads on
$\mathbb{P}^1\times\cdots\times\mathbb{P}^1\times\mathbb{P}^3\times\cdots\times\mathbb{P}^3\times\mathbb{P}^5\times\cdots\times\mathbb{P}^5$.
We proceed to prove stability of the kernel bundle associated to the monad and
simplicity of the cohomology vector bundle. Lastly we establish the existence
of monads on $\mathbb{P}^{a_1}\times\cdots\times\mathbb{P}^{a_n}$ where
$a_1<a_2<\ldots<a_n$, alternating even and odd or at least $a_i$ $0<i\leq{n}$
is odd.
