This paper introduces a novel idea for representation of individuals using quaternions in swarm intelligence and evolutionary algorithms. Quaternions are a number system, which extends complex numbers. They are successfully applied to problems of theoretical physics and to those areas needing fast rotation calculations. We propose the application of quaternions in optimization, more precisely, we have been using quaternions for representation of individuals in Bat algorithm. The preliminary results of our experiments when optimizing a test-suite consisting of ten standard functions showed that this new algorithm significantly improved the results of the original Bat algorithm. Moreover, the obtained results are comparable with other swarm intelligence and evolutionary algorithms, like the artificial bees colony, and differential evolution. We believe that this representation could also be successfully applied to other swarm intelligence and evolutionary algorithms.