Neutron clustering, which is induced by the spatial correlations between neutrons belonging to the same family, is known to cause fluctuations and instabilities in certain types of Monte Carlo neutron transport simulations. The traditional method of sampling branching collision events in Monte Carlo simulations increases these spatial correlations, as multiple particles can be emitted at any given collision site. In this paper, we propose the use of branchless collisions, where only one particle is emitted from a collision site, as a method to reduce neutron clustering in k-eigenvalue power iteration problems. We compare the branchless collision method to the traditional branching method in a simple benchmark, for which analytical solutions can be computed. Our results indicate that branchless collisions can effectively quench neutron clustering.