Replacement of the toxic heavy element lead in metal halide perovskites has been attracting a great interest because the high toxicity and poor air stability are two of the major barriers for their widespread utilization. Recently, mixed-cation double perovskite halides, also known as elpasolites, were proposed as an alternative lead-free candidate for the design of nontoxic perovskite solar cells. Herein, we report a new nontoxic and air stable lead-free all-inorganic semiconductor Rb4Ag2BiBr9 prepared using the mixed cation approach; however, Rb4Ag2BiBr9 adopts a new structure type (Pearson's code oP32) featuring BiBr6 octahedra and AgBr5 square pyramids that share common edges and corners to form a unique 2D layered non-perovskite structure. Rb4Ag2BiBr9 is also demonstrated to be thermally stable with the measured onset decomposition temperature of T-o = 520 degrees C. Optical absorption measurements and density functional theory calculations suggest a nearly direct band gap for Rb4Ag2BiBr9. Room temperature photoluminescence (PL) measurements show a broadband weak emission. Further, temperature-dependent and power-dependent PL measurements show a strong competition between multiple emission centers and suggest the coexistence of defect-bound excitons and self-trapped excitons in Rb4Ag2BiBr9.