Summary: Given any nonzero entire function \(g: \mathbb{C}\to\mathbb{C}\), the complex linear space \(\mathcal{F}(g)\) consists of all entire functions \(f\) decomposable as \(f(z + w)g(z - w)=\phi_1(z)\psi_1(w)+ \phi_n(z)\psi_n(w)\) for some \(\phi_1, \psi_1, \dots, \phi_n, \psi_n: \mathbb{C}\to\mathbb{C}\). The rank of \(f\) with respect to \(g\) is defined as the minimum integer \(n\) for which such a decomposition is possible. It is proved that if \(g\) is an odd function, then the rank any function in \(\mathcal{F}(g)\) is even.