A widely used polarizer in the IR is the wire-grid polarizer. Wire-grid polarizers with a typical minimal wire spacing of ,0.25 mm perform well in the middle IR and the far IR, but in the near IR the performance deteriorates as the wavelength approaches the wire spacing. A possibility for improving this performance is to put two wire grids in tandem with their transmission axes parallel. Starting with the extended Mueller matrix description for a single wire grid, we present a mathematical treatment of this tandem polarizer showing that performance improves quadratically; e.g., a single polarizer extinction ratio of 100 increases to a tandem extinction of 10,000. The improved performance is also verified experimentally.