The paper is introducing the principles of a new global optimization method, No Speeds and Coefficients Particle Swarm Optimization (NSC-PSO), applied to approaching the Continuous Global Optimization Problem (CGOP). Inspired from existing meta-heuristic optimization methods in the Swarm Intelligence (SI) class, like canonical Particle Swarm Optimization (cPSO) and Artificial Bee Colony (ABC), the proposed two versions of the NSC-PSO method are improving over cPSO by eliminating the need of using the speeds of the particles and the coefficients specific to the method. For proving the competitiveness of the proposed NSC-PSO versions they are compared with the ABC method on a test bed of 10 known multimodal optimization problems by applying an appropriate testing methodology. The experimental results showed overall increased efficiency and in many cases improved success rates of the NSC-PSO versions over the ABC method and demonstrated that the proposed NSC-PSO versions are promising approaches to CGOP.