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.