Collision attack is an effective method in the field of side-channel analysis to crack cryptographic algorithms, and masking can be used as a countermeasure. Most collision attacks only utilize the traces that will collide. In this paper, we propose a collision attack method that exploits not only traces tending to collide, but also non-colliding traces. It can bring higher efficiency and reduce the number of needed traces significantly. In addition, our method is a random-plaintext collision attack method instead of a chosen-plaintext attack. The experimental results show that our proposed approach is better than the existing collision-correlation attack proposed by Clavier et al. at CHES 2011 [11]. To achieve a high key recovery success rate at 80%, we use at least 60% less traces than collision-correlation attack.