To discover a common and conserved pattern, or motif, from DNA sequences is an important step to analyze DNA sequences because the patterns are acknowledged to reflect biological important information. However, it is difficult to discover unknown motifs from DNA sequences because of its huge number of combination. We have already proposed a new effective method to extract the motifs using a chaotic search, which combines a heuristic algorithm and a chaotic dynamics. To realize the chaotic search, we used a chaotic neural network. The chaotic search exhibits higher performance than conventional methods. Although we have indicated that the refractory effects realized by the chaotic neural network have an essential role, we did not clarify why the refractory effects are important to search optimal solutions. In this paper, we further investigate this issue and reveal the validity of the refractory effects of the chaotic dynamics using surrogate refractory effects. As a result, we discovered that it is important for searching optimal solutions to increase strength of the refractory effects after a firing of neurons.