Competitive particle swarm optimizer (ComPSO) is a novel swarm intelligence algorithm that does not need any memory. Different from the canonical particle swarm optimizer (PSO), neither gbest nor pbest needs to be stored in ComPSO, and the algorithm is extremely simple in implementation. ComPSO has shown to be highly scalable to the search dimension. In the original ComPSO, two particles are randomly chosen to compete. This work investigates the influence of the competition rule on the search performance of ComPSO and proposes a new competition rule operating on a sorted swarm with neighborhood control. Empirical studies have been performed on a set of widely used test functions to compare the new competition rule with the random strategy. Results show that the new competition rule can speed up the convergence with a big neighborhood size, while with a small neighborhood size, the convergence speed can be slowed down.