A rational rotation algebra $A_\theta $ is a universal $C^*$-algebra generated by two unitaries $U, V$ with relation $VU=\rho UV$, where $\rho=e^{2\pi i\theta}, 0\leq \theta \leq 1$ is rational. Any involutary antiautomorphism of a rational rotation algebra is corresponding to an involution of the torus $T^2$, the spectrum of rational rotation algebra. In this paper, we prove that there is no involutory antiautomorphism in $A_\theta $ associated with the involution $\tau_{_1}:(\lambda, \mu)\mapsto (-\lambda, \mu)$ of the torus.