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We propose an all-optical polarization-insensitive time-division demultiplexer using a nonlinear optical-loop mirror (NOLM) with a pair of short polarization maintaining (PM) fibers. This configuration enables us to realize polarization-diversity operation of a conventional NOLM consisting of a non-PM fiber. When a signal pulse is launched on a PM fiber placed at the input port of the NOLM, the pulse is temporally separated into two pulses with orthogonal linear polarizations. Each polarization component is switched independently by the NOLM, and recombined by another piece of a PM fiber placed at the output port of the NOLM. We experimentally demonstrate that a 40-Gb/s signal is demultiplexed into 10-Gb/s channels independently of. signal polarizations.