Riemann's hypothesis ([1],[2],[3],[6]) , formulated in 1859, concerns the location of the zeros of Riemann's Zeta function. The history of the Riemann Hypothesis is well known. In 1859, the German mathematician B. Riemann presented a paper to the Berlin Academy of Mathematic. In that paper, he proposed that this function, called Riemann-zeta function takes values 0 on the complex plane when s=0.5+it . This hypothesis has great significance for the world of mathematics and physics.([4]) This solutions would lead to innumerable completions of theorems that rely upon its truth. Over a billion zeros of the function have been calculated by computers and shown that all are on this line s = 0.5+it. In this paper we show that Riemann's function (xi) ��, involving the Riemann’s (zeta) �� function, is holomorphic and is expressed as an infinite polynom product in relation to their zeros and their conjugates.([5],[7]) By applying the functional equation of symmetry ��(1 − ��) = ��(��) , we deduce a relation between each zero of the function �� and its conjugate. We obtain the searched result: the real part of all zeros is equal to 1/2.