In this paper, a new particle swarm optimization method (NPSO) is proposed. It is compared with the regular particle swarm optimizer (PSO) invented by Kennedy and Eberhart in 1995 based on four different benchmark functions. PSO is motivated by the social behavior of organisms, such as bird flocking and fish schooling. Each particle studies its own previous best solution to the optimization problem, and its group's previous best, and then adjusts its position (solution) accordingly. The optimal value will be found by repeating this process. In the NPSO proposed here, each particle adjusts its position according to its own previous worst solution and its group's previous worst to find the optimal value. The strategy here is to avoid a particle's previous worst solution and its group's previous worst based on similar formulae of the regular PSO. Under all test cases, simulation shows that the NPSO always finds better solutions than PSO.