This article presents a novel algorithm for multiple odor source localization by a multi-robot system based on a virtual cancelation plume approach. The proposed method is based on rendering a previously declared odor source invisible to the robots so that the declared source and the odor plume it generates do not interfere with the effects of other existing plumes, allowing the localization of the remaining sources. Exploration and plume tracking by the robots is achieved using a decentralized asynchronous particle swarm optimization algorithm. The divergence operator is used to declare the odor sources. A set of simulations and real world experiments are performed on two different scenarios on a controlled environment using a swarm of 5 robots to validate the proposed methodology. Results show that the virtual plume cancelation algorithm can be successfully used to find multiple odor sources, even when two plumes overlap. It can also extend the operation of many odor source localization algorithms developed for single source localization.