Deep neural networks are widely known to be vulnerable to adversarial examples, especially showing significantly poor performance on adversarial examples generated under the white-box setting. However, most white-box attack methods rely heavily on the target model and quickly get stuck in local optima, resulting in poor adversarial transferability. The momentum-based methods and their variants are proposed to escape the local optima for better transferability. In this work, we notice that the transferability of adversarial examples generated by the iterative fast gradient sign method (I-FGSM) exhibits a decreasing trend when increasing the number of iterations. Motivated by this finding, we argue that the information of adversarial perturbations near the benign sample, especially the direction, benefits more on the transferability. Thus, we propose a novel strategy, which uses the Scheduled step size and the Dual example (SD), to fully utilize the adversarial information near the benign sample. Our proposed strategy can be easily integrated with existing adversarial attack methods for better adversarial transferability. Empirical evaluations on the standard ImageNet dataset demonstrate that our proposed method can significantly enhance the transferability of existing adversarial attacks.