When a model checker cannot explore the entire state space because of limited resources, model checking becomes a kind of testing with an attempt to find a failure (violation of properties) quickly. We consider two state sequences in model checking: (i) the sequence in which new states are generated, and (ii) the sequence in which the states generated in sequence (i) are checked for property violation. We observe that neighboring states in sequence (i) often have similarities in certain ways. Based on this observation we propose a search strategy, which generates sequence (ii) in such a way that similar states are evenly spread over the sequence. As a result, neighboring states in sequence (ii) can have a higher diversity. A pilot empirical study with Java PathFinder suggests that the proposed strategy can outperform random search in terms of creating equal or smaller number of states to detect a failure.