The Riemann Hypothesis (RH) is proved based on a new expression of the completed zeta function ξ(s), which was obtained through pairing the conjugate zero ρρi and ρi‾ in the Hadamard product, with consideration of zero multiplicity, i.e. \( \xi(s)=\xi(0)\prod_{\rho}(1-\frac{s}{\rho})=\xi(0)\prod_{i=1}^{\infty}(1-\frac{s}{\rho_i})(1-\frac{s}{\bar{\rho}_i})=\xi(0)\prod_{i=1}^{\infty}\Big{(}\frac{\beta_i^2}{\alpha_i^2+\beta_i^2}+\frac{(s-\alpha_i)^2}{\alpha_i^2+\beta_i^2}\Big{)}^{m_{i}} \), wheree \( \xi(0)=\frac{1}{2} \), \( \rho_i=\alpha_i+j\beta_i \), \( \bar{\rho}_i=\alpha_i-j\beta_i \), with \( 0<\alpha_i<1, \beta_i\neq 0, 0<|\beta_1|\leq|\beta_2|\leq \cdots \), and \( m_i ≥ 1 \) is the multiplicity of \( \rho_i \). Then, according to the functional equation \( \xi(s)=\xi(1-s) \), we obtain \( \prod_{i=1}^{\infty}\Big{(}1+\frac{(s-\alpha_i)^2}{\beta_i^2}\Big{)}^{m_{i}}=\prod_{i=1}^{\infty}\Big{(}1+\frac{(1-s-\alpha_i)^2}{\beta_i^2}\Big{)}^{m_{i}} \), which is finally equivalent to\( \alpha_i=\frac{1}{2}, 0<|\beta_1|<|\beta_2|<|\beta_3|<\cdots, i=1, 2, 3, \dots \) Thus, we conclude that the Riemann Hypothesis is true.