  The subgradient extragradient method for solving the variational inequality
(VI) problem, which is introduced by Censor et al. \cite{CGR}, replaces the
second projection onto the feasible set of the VI, in the extragradient method,
with a subgradient projection onto some constructible half-space. Since the
method has been introduced, many authors proposed extensions and modifications
with applications to various problems.
  In this paper, we introduce a modified subgradient extragradient method by
improving the stepsize of its second step. Convergence of the proposed method
is proved under standard and mild conditions and primary numerical experiments
illustrate the performance and advantage of this new subgradient extragradient
variant.
