A linear-matrix-inequality-based (LMI-based) algorithm is developed to stabilize polytopic systems via static output feedback. The algorithm is termed non-iterative in LMI solutions because, unlike previous LMI-based static-output-feedback algorithms, a finite series of LMI problems are solved without the necessity to repeat the solution to any one of the LMI problems. The algorithm is demonstrated on example problems and numerical experiments borrowed from the literature.