  In this paper, we consider polynomial correspondences $f (x, y)$ in
$\mathbb{C}[x, y]$ of degree $d \ge 2$ in both the variables and obtain
necessary and sufficient conditions in order that the equation $f (x, y) = 0$
can be expressed as $\phi (x) = \psi (y)$, where $\phi$ and $\psi$ are
fractional degree $d$ rational maps in the Riemann sphere. In the absence of
involutions that played a vital role towards characterising quadratic
correspondences ($d = 2$), we employ certain elementary ideas from theory of
equations and matrices to achieve our results. We further explore certain
symmetry conditions on the matrix of coefficients of correspondences that
satisfy the above factorisation. We conclude this short note with a few
examples.
