We prove that $\Im\Big(\frac{\zeta(s)}{s}\Big)+\Im\Big(\frac{\zeta(1-s)}{1-s}\Big)\neq 0$ for every $\Re(s)\in(0,\frac{1}{2})$ and $\Im(s)\in\mathbb{R}^*$, where $\zeta$ is the Riemann Zeta function. In the end of the paper, we give a discussion about the Riemann hypothesis.