We address the problem of identifying the best arm in a pure-exploration multi-armed bandit problem. In this setting, the agent repeatedly pulls arms in order to identify the one associated with the maximum expected reward. We focus on the fixed-budget version of the problem in which the agent tries to find the best arm given a fixed number of arm pulls. We propose a novel sequential elimination method exploiting the empirical variance of the arms. We detail and analyse the overall approach providing theoretical and empirical results. The experimental evaluation shows the advantage of our variance-based rejection method in heterogeneous test settings, considering both identification accuracy and execution time.