This paper describes a method for improving the final accuracy and the convergence speed of Particle Swarm Optimization (PSO) by adapting its inertia factor in the velocity updating equation and also by adding a new coefficient to the position updating equation. These modifications do not impose any serious requirements on the basic algorithm in terms of the number of Function Evaluations (FEs). The new algorithm has been shown to be statistically significantly better than four recent variants of PSO on an eight-function test-suite for the following performance matrices: Quality of the final solution, time to find out the solution, frequency of hitting the optima, and scalability.