Since the proposal of Particle Swarm Optimization (PSO), there have been many improvements of PSO which have not change the basic paradigm of PSO involving pattern of movement of particles, update mode of particles and algorithm framework. Instead of another improvement of PSO, a novel paradigm of PSO with more natural and simpler forms, called naive PSO, is proposed, based on a slightly different social metaphor from that of the original PSO: each particle learns from better one in the swarm and takes warning from worse one in the swarm. In the naive PSO, pattern of movement and mode of update of particles differing from that in the original PSO is introduced. After an algorithm framework is presented, stochastic parameter analysis is also carried out. Preliminary computational experiences show that the naive PSO has a competitive performance over the standard PSO. And then two modifications of the naive PSO are devised. Combining the two modifications, the improved naive PSO shows significantly superior performance over the standard PSO and competitive performance over differential evolution.