Particle Swarm Optimization (PSO) has recently emerged as a nature inspired algorithm for real parameter optimization. This article describes a method for improving the final accuracy and the convergence speed of PSO by adding a new coefficient to the position updating equation and modulating the inertia weight. This work also mathematically analyzes the effect of this modification on the PSO algorithm. The new algorithm has been shown to be statistically significantly better than four recent variants of PSO on a six-functions testsuite.