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By Borel's description, the mod 2 cohomology of a real flag manifold is isomorphic to a polynomial algebra modulo a certain ideal $I$. In this talk we present a new generating set $G$ for $I$. Furthermore, we pose a conjecture on the additive basis of this cohomology (this conjecture is true for many special types of flag manifolds, for example Grassmann manifolds) and prove that $G$ is a Gr\"{o}bner basis for $I$ if and only if this conjecture is true.