The element distinctness problem consists in finding, given a list of elements, if there is some collision (two or more equal elements). The quantum algorithm for element distinctness was first proposed by Ambainis and uses important concepts of quantum walks. Ambainis' algorithm performs a quantum walk over the edges of a Johnson graph while searches for a marked vertex. Szegedy generalized this process into a quantum walk model on bipartite graphs, leading to the formulation of other important algorithms. Recently, Portugal et al. introduced the staggered quantum walk, a novel quantum walk model which includes Szegedy's model as a particular case. In this work, we reformulate the element distinctness quantum algorithm using a staggered quantum walk. We show that our new formulation requires less memory than the original one while keeping the same query complexity.