Let $G = Z_2$. Let X be any compact connected orientable nonsingular real algebraic variety of dim X = k = odd with the trivial G action, and let Y be the unit sphere $S^{2n-k}$ with the antipodal action of G. Then we prove that any G invariant entire rational map $f : x imes Y o S^{2n}$ is G homotopically trivial. We apply this result to prove that any entire rational map $g : X imes RP^{2n-k} o S^{2n}$ is homotopically trivial.